[{"abstract":[{"lang":"eng","text":"We introduce a model of information dissemination in signed networks. It is a discrete-time process in which uninformed actors incrementally receive information from their informed neighbors or from the outside. Our goal is to minimize the number of confused actors — that is, the number of actors who receive contradictory information. We prove upper bounds for the number of confused actors in signed networks and in equivalence classes of signed networks. In particular, we show that there are signed networks where, for any information placement strategy, almost 60% of the actors are confused. Furthermore, this is also the case when considering the minimum number of confused actors within an equivalence class of signed graphs."}],"status":"public","type":"journal_article","publication":"Discrete Applied Mathematics","language":[{"iso":"eng"}],"_id":"59806","user_id":"15540","department":[{"_id":"542"}],"year":"2025","citation":{"ama":"Jin L, Steffen E. Information dissemination and confusion in signed networks. <i>Discrete Applied Mathematics</i>. 2025;373:99-106. doi:<a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>","ieee":"L. Jin and E. Steffen, “Information dissemination and confusion in signed networks,” <i>Discrete Applied Mathematics</i>, vol. 373, pp. 99–106, 2025, doi: <a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>.","chicago":"Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion in Signed Networks.” <i>Discrete Applied Mathematics</i> 373 (2025): 99–106. <a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">https://doi.org/10.1016/j.dam.2025.04.049</a>.","apa":"Jin, L., &#38; Steffen, E. (2025). Information dissemination and confusion in signed networks. <i>Discrete Applied Mathematics</i>, <i>373</i>, 99–106. <a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">https://doi.org/10.1016/j.dam.2025.04.049</a>","bibtex":"@article{Jin_Steffen_2025, title={Information dissemination and confusion in signed networks}, volume={373}, DOI={<a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>}, journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Jin, Ligang and Steffen, Eckhard}, year={2025}, pages={99–106} }","short":"L. Jin, E. Steffen, Discrete Applied Mathematics 373 (2025) 99–106.","mla":"Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion in Signed Networks.” <i>Discrete Applied Mathematics</i>, vol. 373, Elsevier BV, 2025, pp. 99–106, doi:<a href=\"https://doi.org/10.1016/j.dam.2025.04.049\">10.1016/j.dam.2025.04.049</a>."},"intvolume":"       373","page":"99-106","publication_status":"published","publication_identifier":{"issn":["0166-218X"]},"title":"Information dissemination and confusion in signed networks","doi":"10.1016/j.dam.2025.04.049","date_updated":"2025-05-06T07:39:58Z","publisher":"Elsevier BV","author":[{"last_name":"Jin","full_name":"Jin, Ligang","first_name":"Ligang"},{"orcid":"0000-0002-9808-7401","last_name":"Steffen","full_name":"Steffen, Eckhard","id":"15548","first_name":"Eckhard"}],"date_created":"2025-05-06T07:38:49Z","volume":373},{"language":[{"iso":"eng"}],"publication":"Combinatorica","abstract":[{"text":"An r-regular graph is an r-graph, if every odd set of vertices is connected to its complement by at least r edges. Let G and H be r-graphs. An H-coloring of G is a mapping such that each r adjacent edges of G are mapped to r adjacent edges of H. For every , let be an inclusion-wise minimal set of connected r-graphs, such that for every connected r-graph G there is an which colors G. The Petersen Coloring Conjecture states that consists of the Petersen graph P. We show that if true, then this is a very exclusive situation. Our main result is that either or is an infinite set and if , then is an infinite set. In particular, for all , is unique. We first characterize and then prove that if contains more than one element, then it is an infinite set. To obtain our main result we show that contains the smallest r-graphs of class 2 and the smallest poorly matchable r-graphs, and we determine the smallest r-graphs of class 2.","lang":"eng"}],"date_created":"2025-03-27T09:46:34Z","publisher":"Springer Science and Business Media LLC","title":"Sets of r-Graphs that Color All r-Graphs","issue":"2","year":"2025","department":[{"_id":"542"}],"user_id":"15540","_id":"59169","article_number":"16","type":"journal_article","status":"public","volume":45,"author":[{"full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai"},{"first_name":"Davide","last_name":"Mattiolo","full_name":"Mattiolo, Davide"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548"},{"first_name":"Isaak H.","last_name":"Wolf","full_name":"Wolf, Isaak H."}],"date_updated":"2025-03-27T09:48:48Z","doi":"10.1007/s00493-025-00144-4","publication_identifier":{"issn":["0209-9683","1439-6912"]},"publication_status":"published","intvolume":"        45","citation":{"chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak H. Wolf. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i> 45, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-Graphs that Color All r-Graphs,” <i>Combinatorica</i>, vol. 45, no. 2, Art. no. 16, 2025, doi: <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>. 2025;45(2). doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2025). Sets of r-Graphs that Color All r-Graphs. <i>Combinatorica</i>, <i>45</i>(2), Article 16. <a href=\"https://doi.org/10.1007/s00493-025-00144-4\">https://doi.org/10.1007/s00493-025-00144-4</a>","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2025, title={Sets of r-Graphs that Color All r-Graphs}, volume={45}, DOI={<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>}, number={216}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak H.}, year={2025} }","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 45 (2025).","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>Combinatorica</i>, vol. 45, no. 2, 16, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00493-025-00144-4\">10.1007/s00493-025-00144-4</a>."}},{"abstract":[{"lang":"eng","text":"We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs."}],"status":"public","publication":"Journal of Algebraic Combinatorics","type":"journal_article","article_number":"7","language":[{"iso":"eng"}],"_id":"61042","department":[{"_id":"542"}],"user_id":"15540","year":"2025","intvolume":"        62","citation":{"short":"C. Dalfó, M.A. Fiol, E. Steffen, Journal of Algebraic Combinatorics 62 (2025).","mla":"Dalfó, C., et al. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, 7, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>.","bibtex":"@article{Dalfó_Fiol_Steffen_2025, title={On token signed graphs}, volume={62}, DOI={<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>}, number={17}, journal={Journal of Algebraic Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2025} }","apa":"Dalfó, C., Fiol, M. A., &#38; Steffen, E. (2025). On token signed graphs. <i>Journal of Algebraic Combinatorics</i>, <i>62</i>(1), Article 7. <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>","chicago":"Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” <i>Journal of Algebraic Combinatorics</i> 62, no. 1 (2025). <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">https://doi.org/10.1007/s10801-025-01416-4</a>.","ieee":"C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” <i>Journal of Algebraic Combinatorics</i>, vol. 62, no. 1, Art. no. 7, 2025, doi: <a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>.","ama":"Dalfó C, Fiol MA, Steffen E. On token signed graphs. <i>Journal of Algebraic Combinatorics</i>. 2025;62(1). doi:<a href=\"https://doi.org/10.1007/s10801-025-01416-4\">10.1007/s10801-025-01416-4</a>"},"publication_identifier":{"issn":["0925-9899","1572-9192"]},"publication_status":"published","issue":"1","title":"On token signed graphs","doi":"10.1007/s10801-025-01416-4","publisher":"Springer Science and Business Media LLC","date_updated":"2025-08-28T07:57:27Z","volume":62,"author":[{"last_name":"Dalfó","full_name":"Dalfó, C.","first_name":"C."},{"full_name":"Fiol, M. A.","last_name":"Fiol","first_name":"M. A."},{"first_name":"Eckhard","id":"15548","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen"}],"date_created":"2025-08-28T07:50:03Z"},{"status":"public","type":"preprint","publication":"arXiv:2512.14285","language":[{"iso":"eng"}],"user_id":"15540","department":[{"_id":"542"}],"_id":"63187","external_id":{"arxiv":["2512.14285"]},"citation":{"apa":"Kidner, A. J. J., Steffen, E., &#38; Yu, W. (2025). Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. In <i>arXiv:2512.14285</i>.","mla":"Kidner, Arnott Jeffery Joel, et al. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.","bibtex":"@article{Kidner_Steffen_Yu_2025, title={Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor}, journal={arXiv:2512.14285}, author={Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}, year={2025} }","short":"A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).","ieee":"A. J. J. Kidner, E. Steffen, and W. Yu, “Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor,” <i>arXiv:2512.14285</i>. 2025.","chicago":"Kidner, Arnott Jeffery Joel, Eckhard Steffen, and Weiqiang Yu. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.","ama":"Kidner AJJ, Steffen E, Yu W. Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. <i>arXiv:251214285</i>. Published online 2025."},"year":"2025","title":"Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor","date_created":"2025-12-17T14:40:23Z","author":[{"first_name":"Arnott Jeffery Joel","last_name":"Kidner","full_name":"Kidner, Arnott Jeffery Joel","id":"111755"},{"first_name":"Eckhard","full_name":"Steffen, Eckhard","id":"15548","orcid":"0000-0002-9808-7401","last_name":"Steffen"},{"first_name":"Weiqiang","last_name":"Yu","id":"117508","full_name":"Yu, Weiqiang"}],"date_updated":"2025-12-18T13:17:18Z"},{"title":"Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs","doi":"10.1007/s00493-023-00078-9","publisher":"Springer Science and Business Media LLC","date_updated":"2024-03-22T12:11:35Z","author":[{"first_name":"Yulai","last_name":"Ma","id":"92748","full_name":"Ma, Yulai"},{"first_name":"Davide","last_name":"Mattiolo","full_name":"Mattiolo, Davide"},{"orcid":"0000-0002-9808-7401","last_name":"Steffen","id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard"},{"first_name":"Isaak Hieronymus","id":"88145","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf"}],"date_created":"2023-12-20T10:31:27Z","volume":44,"year":"2024","citation":{"ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs,” <i>Combinatorica</i>, vol. 44, pp. 429–440, 2024, doi: <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>.","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” <i>Combinatorica</i> 44 (2024): 429–40. <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">https://doi.org/10.1007/s00493-023-00078-9</a>.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>. 2024;44:429-440. doi:<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2024). Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>, <i>44</i>, 429–440. <a href=\"https://doi.org/10.1007/s00493-023-00078-9\">https://doi.org/10.1007/s00493-023-00078-9</a>","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.","mla":"Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” <i>Combinatorica</i>, vol. 44, Springer Science and Business Media LLC, 2024, pp. 429–40, doi:<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={<a href=\"https://doi.org/10.1007/s00493-023-00078-9\">10.1007/s00493-023-00078-9</a>}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2024}, pages={429–440} }"},"intvolume":"        44","page":"429-440","publication_status":"published","publication_identifier":{"issn":["0209-9683","1439-6912"]},"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"language":[{"iso":"eng"}],"_id":"49905","user_id":"15540","department":[{"_id":"542"}],"abstract":[{"lang":"eng","text":"For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t \u0003 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l."}],"status":"public","type":"journal_article","publication":"Combinatorica"},{"department":[{"_id":"542"}],"user_id":"15540","_id":"56497","language":[{"iso":"eng"}],"article_number":"114258","publication":"Discrete Mathematics","type":"journal_article","status":"public","volume":348,"date_created":"2024-10-10T12:27:11Z","author":[{"full_name":"Cappello, Chiara","last_name":"Cappello","first_name":"Chiara"},{"first_name":"Reza","last_name":"Naserasr","full_name":"Naserasr, Reza"},{"orcid":"0000-0002-9808-7401","last_name":"Steffen","full_name":"Steffen, Eckhard","id":"15548","first_name":"Eckhard"},{"full_name":"Wang, Zhouningxin","last_name":"Wang","first_name":"Zhouningxin"}],"date_updated":"2024-10-10T12:28:13Z","publisher":"Elsevier BV","doi":"10.1016/j.disc.2024.114258","title":"Critically 3-frustrated signed graphs","issue":"1","publication_identifier":{"issn":["0012-365X"]},"publication_status":"published","intvolume":"       348","citation":{"chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” <i>Discrete Mathematics</i> 348, no. 1 (2024). <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">https://doi.org/10.1016/j.disc.2024.114258</a>.","ieee":"C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” <i>Discrete Mathematics</i>, vol. 348, no. 1, Art. no. 114258, 2024, doi: <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>.","ama":"Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. <i>Discrete Mathematics</i>. 2024;348(1). doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>","bibtex":"@article{Cappello_Naserasr_Steffen_Wang_2024, title={Critically 3-frustrated signed graphs}, volume={348}, DOI={<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>}, number={1114258}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2024} }","short":"C. Cappello, R. Naserasr, E. Steffen, Z. Wang, Discrete Mathematics 348 (2024).","mla":"Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” <i>Discrete Mathematics</i>, vol. 348, no. 1, 114258, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>.","apa":"Cappello, C., Naserasr, R., Steffen, E., &#38; Wang, Z. (2024). Critically 3-frustrated signed graphs. <i>Discrete Mathematics</i>, <i>348</i>(1), Article 114258. <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">https://doi.org/10.1016/j.disc.2024.114258</a>"},"year":"2024"},{"keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics"],"language":[{"iso":"eng"}],"_id":"51351","department":[{"_id":"542"}],"user_id":"15540","status":"public","publication":"Discrete Applied Mathematics","type":"journal_article","title":"Bounds for the chromatic index of signed multigraphs","doi":"10.1016/j.dam.2023.05.008","date_updated":"2024-02-14T17:33:59Z","publisher":"Elsevier BV","volume":337,"author":[{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","id":"15548","full_name":"Steffen, Eckhard"},{"first_name":"Isaak Hieronymus","last_name":"Wolf","id":"88145","full_name":"Wolf, Isaak Hieronymus"}],"date_created":"2024-02-14T17:33:29Z","year":"2023","page":"185-189","intvolume":"       337","citation":{"apa":"Steffen, E., &#38; Wolf, I. H. (2023). Bounds for the chromatic index of signed multigraphs. <i>Discrete Applied Mathematics</i>, <i>337</i>, 185–189. <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">https://doi.org/10.1016/j.dam.2023.05.008</a>","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i>, vol. 337, Elsevier BV, 2023, pp. 185–89, doi:<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>.","short":"E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.","bibtex":"@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed multigraphs}, volume={337}, DOI={<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>}, journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }","chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i> 337 (2023): 185–89. <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">https://doi.org/10.1016/j.dam.2023.05.008</a>.","ieee":"E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,” <i>Discrete Applied Mathematics</i>, vol. 337, pp. 185–189, 2023, doi: <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>.","ama":"Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. <i>Discrete Applied Mathematics</i>. 2023;337:185-189. doi:<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>"},"publication_identifier":{"issn":["0166-218X"]},"publication_status":"published"},{"author":[{"first_name":"Chiara","id":"72874","full_name":"Cappello, Chiara","last_name":"Cappello"},{"last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548","first_name":"Eckhard"}],"date_created":"2023-05-22T10:22:21Z","publisher":"Springer International Publishing","date_updated":"2024-02-16T07:42:38Z","doi":"10.1007/978-3-031-26104-6_5","title":"Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks","publication_identifier":{"isbn":["9783031261039","9783031261046"]},"publication_status":"published","page":"93--110","citation":{"ieee":"C. Cappello and E. Steffen, “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks,” in <i>The Digital Twin of Humans</i>, Cham: Springer International Publishing, 2023, pp. 93--110.","chicago":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” In <i>The Digital Twin of Humans</i>, 93--110. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">https://doi.org/10.1007/978-3-031-26104-6_5</a>.","ama":"Cappello C, Steffen E. Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In: <i>The Digital Twin of Humans</i>. Springer International Publishing; 2023:93--110. doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>","bibtex":"@inbook{Cappello_Steffen_2023, place={Cham}, title={Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>}, booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing}, author={Cappello, Chiara and Steffen, Eckhard}, year={2023}, pages={93--110} }","mla":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” <i>The Digital Twin of Humans</i>, Springer International Publishing, 2023, pp. 93--110, doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>.","short":"C. Cappello, E. Steffen, in: The Digital Twin of Humans, Springer International Publishing, Cham, 2023, pp. 93--110.","apa":"Cappello, C., &#38; Steffen, E. (2023). Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In <i>The Digital Twin of Humans</i> (pp. 93--110). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">https://doi.org/10.1007/978-3-031-26104-6_5</a>"},"place":"Cham","year":"2023","department":[{"_id":"542"}],"user_id":"15540","_id":"45190","language":[{"iso":"eng"}],"publication":"The Digital Twin of Humans","type":"book_chapter","status":"public"},{"_id":"51357","user_id":"15540","department":[{"_id":"542"}],"article_number":"113457","keyword":["Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Discrete Mathematics","status":"public","date_updated":"2024-02-16T08:45:10Z","publisher":"Elsevier BV","date_created":"2024-02-16T08:44:50Z","author":[{"id":"15548","full_name":"Steffen, Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","first_name":"Eckhard"},{"id":"88145","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf","first_name":"Isaak Hieronymus"}],"title":"Rotation r-graphs","doi":"10.1016/j.disc.2023.113457","publication_status":"published","publication_identifier":{"issn":["0012-365X"]},"year":"2023","citation":{"apa":"Steffen, E., &#38; Wolf, I. H. (2023). Rotation r-graphs. <i>Discrete Mathematics</i>, Article 113457. <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">https://doi.org/10.1016/j.disc.2023.113457</a>","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete Mathematics</i>, 113457, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>.","bibtex":"@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>}, number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","short":"E. Steffen, I.H. Wolf, Discrete Mathematics (2023).","ieee":"E. Steffen and I. H. Wolf, “Rotation r-graphs,” <i>Discrete Mathematics</i>, Art. no. 113457, 2023, doi: <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>.","chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete Mathematics</i>, 2023. <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">https://doi.org/10.1016/j.disc.2023.113457</a>.","ama":"Steffen E, Wolf IH. Rotation r-graphs. <i>Discrete Mathematics</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>"}},{"publication_identifier":{"isbn":["9783031261039","9783031261046"]},"publication_status":"published","related_material":{"link":[{"relation":"confirmation","url":"https://link.springer.com/book/10.1007/978-3-031-26104-6"}]},"place":"Cham","page":"3-10","citation":{"apa":"Gräßler, I., Steffen, E., Maier, G. W., &#38; Roesmann, D. (2023). Introduction—The Digital Twin of Humans. In I. Gräßler, G. W. Maier, E. Steffen, &#38; D. Roesmann (Eds.), <i>The Digital Twin of Humans</i> (pp. 3–10). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_1\">https://doi.org/10.1007/978-3-031-26104-6_1</a>","bibtex":"@inbook{Gräßler_Steffen_Maier_Roesmann_2023, place={Cham}, title={Introduction—The Digital Twin of Humans}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-26104-6_1\">10.1007/978-3-031-26104-6_1</a>}, booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing}, author={Gräßler, Iris and Steffen, Eckhard and Maier, Günter W. and Roesmann, Daniel}, editor={Gräßler, Iris and Maier, Günter W. and Steffen, Eckhard and Roesmann, Daniel}, year={2023}, pages={3–10} }","mla":"Gräßler, Iris, et al. “Introduction—The Digital Twin of Humans.” <i>The Digital Twin of Humans</i>, edited by Iris Gräßler et al., Springer International Publishing, 2023, pp. 3–10, doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_1\">10.1007/978-3-031-26104-6_1</a>.","short":"I. Gräßler, E. Steffen, G.W. Maier, D. Roesmann, in: I. Gräßler, G.W. Maier, E. Steffen, D. Roesmann (Eds.), The Digital Twin of Humans, Springer International Publishing, Cham, 2023, pp. 3–10.","chicago":"Gräßler, Iris, Eckhard Steffen, Günter W. Maier, and Daniel Roesmann. “Introduction—The Digital Twin of Humans.” In <i>The Digital Twin of Humans</i>, edited by Iris Gräßler, Günter W. Maier, Eckhard Steffen, and Daniel Roesmann, 3–10. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_1\">https://doi.org/10.1007/978-3-031-26104-6_1</a>.","ieee":"I. Gräßler, E. Steffen, G. W. Maier, and D. Roesmann, “Introduction—The Digital Twin of Humans,” in <i>The Digital Twin of Humans</i>, I. Gräßler, G. W. Maier, E. Steffen, and D. Roesmann, Eds. Cham: Springer International Publishing, 2023, pp. 3–10.","ama":"Gräßler I, Steffen E, Maier GW, Roesmann D. Introduction—The Digital Twin of Humans. In: Gräßler I, Maier GW, Steffen E, Roesmann D, eds. <i>The Digital Twin of Humans</i>. Springer International Publishing; 2023:3-10. doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_1\">10.1007/978-3-031-26104-6_1</a>"},"date_updated":"2024-03-25T09:08:11Z","author":[{"id":"47565","full_name":"Gräßler, Iris","last_name":"Gräßler","orcid":"0000-0001-5765-971X","first_name":"Iris"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","id":"15548","full_name":"Steffen, Eckhard"},{"full_name":"Maier, Günter W.","last_name":"Maier","first_name":"Günter W."},{"last_name":"Roesmann","id":"54680","full_name":"Roesmann, Daniel","first_name":"Daniel"}],"doi":"10.1007/978-3-031-26104-6_1","type":"book_chapter","editor":[{"first_name":"Iris","full_name":"Gräßler, Iris","last_name":"Gräßler"},{"last_name":"Maier","full_name":"Maier, Günter W.","first_name":"Günter W."},{"last_name":"Steffen","full_name":"Steffen, Eckhard","first_name":"Eckhard"},{"full_name":"Roesmann, Daniel","last_name":"Roesmann","first_name":"Daniel"}],"status":"public","_id":"45110","department":[{"_id":"152"}],"user_id":"5905","quality_controlled":"1","year":"2023","publisher":"Springer International Publishing","date_created":"2023-05-18T23:45:04Z","title":"Introduction—The Digital Twin of Humans","publication":"The Digital Twin of Humans","language":[{"iso":"eng"}]},{"publication_status":"published","publication_identifier":{"isbn":["9783031261039","9783031261046"]},"quality_controlled":"1","year":"2023","place":"Cham","citation":{"mla":"Gräßler, Iris, et al., editors. <i>The Digital Twin of Humans</i>. Springer International Publishing, 2023, doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6\">10.1007/978-3-031-26104-6</a>.","short":"I. Gräßler, G.W. Maier, E. Steffen, D. Roesmann, eds., The Digital Twin of Humans, Springer International Publishing, Cham, 2023.","bibtex":"@book{Gräßler_Maier_Steffen_Roesmann_2023, place={Cham}, title={The Digital Twin of Humans}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-26104-6\">10.1007/978-3-031-26104-6</a>}, publisher={Springer International Publishing}, year={2023} }","apa":"Gräßler, I., Maier, G. W., Steffen, E., &#38; Roesmann, D. (Eds.). (2023). <i>The Digital Twin of Humans</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-26104-6\">https://doi.org/10.1007/978-3-031-26104-6</a>","ama":"Gräßler I, Maier GW, Steffen E, Roesmann D, eds. <i>The Digital Twin of Humans</i>. Springer International Publishing; 2023. doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6\">10.1007/978-3-031-26104-6</a>","ieee":"I. Gräßler, G. W. Maier, E. Steffen, and D. Roesmann, Eds., <i>The Digital Twin of Humans</i>. Cham: Springer International Publishing, 2023.","chicago":"Gräßler, Iris, Günter W. Maier, Eckhard Steffen, and Daniel Roesmann, eds. <i>The Digital Twin of Humans</i>. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-26104-6\">https://doi.org/10.1007/978-3-031-26104-6</a>."},"date_updated":"2024-03-25T09:07:55Z","publisher":"Springer International Publishing","date_created":"2023-05-22T10:24:10Z","title":"The Digital Twin of Humans","doi":"10.1007/978-3-031-26104-6","type":"book_editor","editor":[{"full_name":"Gräßler, Iris","id":"47565","last_name":"Gräßler","orcid":"0000-0001-5765-971X","first_name":"Iris"},{"first_name":"Günter W.","last_name":"Maier","full_name":"Maier, Günter W."},{"first_name":"Eckhard","full_name":"Steffen, Eckhard","id":"15548","orcid":"0000-0002-9808-7401","last_name":"Steffen"},{"first_name":"Daniel","id":"54680","full_name":"Roesmann, Daniel","last_name":"Roesmann"}],"status":"public","_id":"45191","user_id":"5905","department":[{"_id":"542"},{"_id":"152"}],"alternative_title":["An Interdisciplinary Concept of Digital Working Environments in Industry 4.0"],"language":[{"iso":"eng"}]},{"_id":"44857","user_id":"15540","department":[{"_id":"542"}],"type":"journal_article","status":"public","date_updated":"2023-05-16T08:49:30Z","author":[{"first_name":"Helmuth O.M.","last_name":"Silva","full_name":"Silva, Helmuth O.M."},{"first_name":"Diego P.","full_name":"Rubert, Diego P.","last_name":"Rubert"},{"full_name":"Araujo, Eloi","last_name":"Araujo","first_name":"Eloi"},{"first_name":"Eckhard","id":"15548","full_name":"Steffen, Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401"},{"last_name":"Doerr","full_name":"Doerr, Daniel","first_name":"Daniel"},{"last_name":"Martinez","full_name":"Martinez, Fábio V.","first_name":"Fábio V."}],"volume":57,"doi":"10.1051/ro/2023052","publication_status":"published","publication_identifier":{"issn":["0399-0559","2804-7303"]},"citation":{"bibtex":"@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms for the genome median under a restricted measure of rearrangement}, volume={57}, DOI={<a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>}, number={3}, journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }","short":"H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez, RAIRO - Operations Research 57 (2023) 1045–1058.","mla":"Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” <i>RAIRO - Operations Research</i>, vol. 57, no. 3, EDP Sciences, 2023, pp. 1045–58, doi:<a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>.","apa":"Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., &#38; Martinez, F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement. <i>RAIRO - Operations Research</i>, <i>57</i>(3), 1045–1058. <a href=\"https://doi.org/10.1051/ro/2023052\">https://doi.org/10.1051/ro/2023052</a>","ama":"Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms for the genome median under a restricted measure of rearrangement. <i>RAIRO - Operations Research</i>. 2023;57(3):1045-1058. doi:<a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>","ieee":"H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V. Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,” <i>RAIRO - Operations Research</i>, vol. 57, no. 3, pp. 1045–1058, 2023, doi: <a href=\"https://doi.org/10.1051/ro/2023052\">10.1051/ro/2023052</a>.","chicago":"Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” <i>RAIRO - Operations Research</i> 57, no. 3 (2023): 1045–58. <a href=\"https://doi.org/10.1051/ro/2023052\">https://doi.org/10.1051/ro/2023052</a>."},"intvolume":"        57","page":"1045-1058","keyword":["Management Science and Operations Research","Computer Science Applications","Theoretical Computer Science"],"language":[{"iso":"eng"}],"publication":"RAIRO - Operations Research","abstract":[{"lang":"eng","text":"Ancestral reconstruction is a classic task in comparative genomics. Here, we study the genome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. The distance stands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of the breakpoint median that can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure called c4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of the c4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that the c4-distance is useful for the study the genome median problem, from theoretical and practical perspectives."}],"publisher":"EDP Sciences","date_created":"2023-05-16T08:48:22Z","title":"Algorithms for the genome median under a restricted measure of rearrangement","issue":"3","year":"2023"},{"citation":{"short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","mla":"Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>, 2023.","apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Sets of r-graphs that color all r-graphs. In <i>arXiv:2305.08619</i>.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs. <i>arXiv:230508619</i>. Published online 2023.","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” <i>arXiv:2305.08619</i>. 2023.","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Sets of R-Graphs That Color All r-Graphs.” <i>ArXiv:2305.08619</i>, 2023."},"year":"2023","author":[{"id":"92748","full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"first_name":"Eckhard","id":"15548","full_name":"Steffen, Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401"},{"first_name":"Isaak Hieronymus","id":"88145","full_name":"Wolf, Isaak Hieronymus","last_name":"Wolf"}],"date_created":"2023-05-16T10:07:47Z","date_updated":"2023-05-16T11:17:26Z","title":"Sets of r-graphs that color all r-graphs","type":"preprint","publication":"arXiv:2305.08619","status":"public","user_id":"15540","department":[{"_id":"542"}],"external_id":{"arxiv":["2305.08619"]},"_id":"44859","language":[{"iso":"eng"}]},{"date_updated":"2023-08-01T10:09:35Z","publisher":"Society for Industrial & Applied Mathematics (SIAM)","date_created":"2023-08-01T10:08:32Z","author":[{"last_name":"Ma","id":"92748","full_name":"Ma, Yulai","first_name":"Yulai"},{"first_name":"Davide","full_name":"Mattiolo, Davide","last_name":"Mattiolo"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","id":"15548","full_name":"Steffen, Eckhard"},{"first_name":"Isaak Hieronymus","last_name":"Wolf","id":"88145","full_name":"Wolf, Isaak Hieronymus"}],"volume":37,"title":"Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs","doi":"10.1137/22m1500654","publication_status":"published","publication_identifier":{"issn":["0895-4801","1095-7146"]},"issue":"3","year":"2023","citation":{"apa":"Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete Mathematics</i>, <i>37</i>(3), 1548–1565. <a href=\"https://doi.org/10.1137/22m1500654\">https://doi.org/10.1137/22m1500654</a>","short":"Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565.","mla":"Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>.","bibtex":"@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }","ieee":"Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3, pp. 1548–1565, 2023, doi: <a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>.","chicago":"Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i> 37, no. 3 (2023): 1548–65. <a href=\"https://doi.org/10.1137/22m1500654\">https://doi.org/10.1137/22m1500654</a>.","ama":"Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete Mathematics</i>. 2023;37(3):1548-1565. doi:<a href=\"https://doi.org/10.1137/22m1500654\">10.1137/22m1500654</a>"},"intvolume":"        37","page":"1548-1565","_id":"46256","user_id":"15540","department":[{"_id":"542"}],"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"SIAM Journal on Discrete Mathematics","status":"public"},{"_id":"33741","external_id":{"arxiv":["2106.05928"]},"department":[{"_id":"542"}],"user_id":"15540","keyword":["Discrete Mathematics and Combinatorics"],"language":[{"iso":"eng"}],"publication":"Annals of Combinatorics","type":"journal_article","abstract":[{"lang":"eng","text":"There are many concepts of signed graph coloring which are defined by assigning colors to the vertices of the graphs. These concepts usually differ in the number of self-inverse colors used. We introduce a unifying concept for this kind of coloring by assigning elements from symmetric sets to the vertices of the signed graphs. In the first part of the paper, we study colorings with elements from symmetric sets where the number of self-inverse elements is fixed. We prove a Brooks’-type theorem and upper bounds for the corresponding chromatic numbers in terms of the chromatic number of the underlying graph. These results are used in the second part where we introduce the symset-chromatic number χsym(G,σ) of a signed graph (G,σ). We show that the symset-chromatic number gives the minimum partition of a signed graph into independent sets and non-bipartite antibalanced subgraphs. In particular, χsym(G,σ)≤χ(G). In the final section we show that these colorings can also be formalized as DP-colorings."}],"status":"public","publisher":"Springer Science and Business Media LLC","date_updated":"2023-05-16T10:37:58Z","date_created":"2022-10-17T07:54:41Z","author":[{"full_name":"Cappello, Chiara","id":"72874","last_name":"Cappello","first_name":"Chiara"},{"full_name":"Steffen, Eckhard","id":"15548","last_name":"Steffen","orcid":"0000-0002-9808-7401","first_name":"Eckhard"}],"title":"Symmetric Set Coloring of Signed Graphs","doi":"10.1007/s00026-022-00593-4","publication_identifier":{"issn":["0218-0006","0219-3094"]},"publication_status":"published","year":"2022","citation":{"short":"C. Cappello, E. Steffen, Annals of Combinatorics (2022).","mla":"Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed Graphs.” <i>Annals of Combinatorics</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s00026-022-00593-4\">10.1007/s00026-022-00593-4</a>.","bibtex":"@article{Cappello_Steffen_2022, title={Symmetric Set Coloring of Signed Graphs}, DOI={<a href=\"https://doi.org/10.1007/s00026-022-00593-4\">10.1007/s00026-022-00593-4</a>}, journal={Annals of Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Cappello, Chiara and Steffen, Eckhard}, year={2022} }","apa":"Cappello, C., &#38; Steffen, E. (2022). Symmetric Set Coloring of Signed Graphs. <i>Annals of Combinatorics</i>. <a href=\"https://doi.org/10.1007/s00026-022-00593-4\">https://doi.org/10.1007/s00026-022-00593-4</a>","ama":"Cappello C, Steffen E. Symmetric Set Coloring of Signed Graphs. <i>Annals of Combinatorics</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s00026-022-00593-4\">10.1007/s00026-022-00593-4</a>","ieee":"C. Cappello and E. Steffen, “Symmetric Set Coloring of Signed Graphs,” <i>Annals of Combinatorics</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s00026-022-00593-4\">10.1007/s00026-022-00593-4</a>.","chicago":"Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed Graphs.” <i>Annals of Combinatorics</i>, 2022. <a href=\"https://doi.org/10.1007/s00026-022-00593-4\">https://doi.org/10.1007/s00026-022-00593-4</a>."}},{"publication_identifier":{"issn":["0911-0119","1435-5914"]},"publication_status":"published","intvolume":"        38","citation":{"ama":"Steffen E, Wolf IH. Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices. <i>Graphs and Combinatorics</i>. 2022;38(3). doi:<a href=\"https://doi.org/10.1007/s00373-022-02506-x\">10.1007/s00373-022-02506-x</a>","ieee":"E. Steffen and I. H. Wolf, “Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices,” <i>Graphs and Combinatorics</i>, vol. 38, no. 3, Art. no. 104, 2022, doi: <a href=\"https://doi.org/10.1007/s00373-022-02506-x\">10.1007/s00373-022-02506-x</a>.","chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices.” <i>Graphs and Combinatorics</i> 38, no. 3 (2022). <a href=\"https://doi.org/10.1007/s00373-022-02506-x\">https://doi.org/10.1007/s00373-022-02506-x</a>.","bibtex":"@article{Steffen_Wolf_2022, title={Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices}, volume={38}, DOI={<a href=\"https://doi.org/10.1007/s00373-022-02506-x\">10.1007/s00373-022-02506-x</a>}, number={3104}, journal={Graphs and Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2022} }","short":"E. Steffen, I.H. Wolf, Graphs and Combinatorics 38 (2022).","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices.” <i>Graphs and Combinatorics</i>, vol. 38, no. 3, 104, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s00373-022-02506-x\">10.1007/s00373-022-02506-x</a>.","apa":"Steffen, E., &#38; Wolf, I. H. (2022). 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Zhang, Journal of Combinatorial Theory, Series B 153 (2021) 61–80.","bibtex":"@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in toroidal graphs}, volume={153}, DOI={<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>}, journal={Journal of Combinatorial Theory, Series B}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}, year={2021}, pages={61–80} }","mla":"Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>.","chicago":"Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i> 153 (2021): 61–80. <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">https://doi.org/10.1016/j.jctb.2021.11.001</a>.","ieee":"J. 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