{"citation":{"apa":"Fiol, M. A., Mazzuoccolo, G., &#38; Steffen, E. (2018). Measures of Edge-Uncolorability of Cubic Graphs. <i>The Electronic Journal of Combinatorics</i>, <i>25</i>(4).","ama":"Fiol MA, Mazzuoccolo G, Steffen E. Measures of Edge-Uncolorability of Cubic Graphs. <i>The Electronic Journal of Combinatorics</i>. 2018;25(4).","mla":"Fiol, M. A., et al. “Measures of Edge-Uncolorability of Cubic Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 25, no. 4, P4.54, 2018.","ieee":"M. A. Fiol, G. Mazzuoccolo, and E. Steffen, “Measures of Edge-Uncolorability of Cubic Graphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 25, no. 4, 2018.","chicago":"Fiol, M. A., Guiseppe Mazzuoccolo, and Eckhard Steffen. “Measures of Edge-Uncolorability of Cubic Graphs.” <i>The Electronic Journal of Combinatorics</i> 25, no. 4 (2018).","short":"M.A. Fiol, G. Mazzuoccolo, E. Steffen, The Electronic Journal of Combinatorics 25 (2018).","bibtex":"@article{Fiol_Mazzuoccolo_Steffen_2018, title={Measures of Edge-Uncolorability of Cubic Graphs}, volume={25}, number={4P4.54}, journal={The Electronic Journal of Combinatorics}, author={Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard}, year={2018} }"},"user_id":"15540","date_created":"2019-06-05T09:59:10Z","department":[{"_id":"542"}],"_id":"10129","keyword":["Cubic graph","Tait coloring","Snark","Boole coloring","Berge's conjecture","Tutte's 5-flow conjecture"],"title":"Measures of Edge-Uncolorability of Cubic Graphs","volume":25,"author":[{"first_name":"M. A.","full_name":"Fiol, M. A.","last_name":"Fiol"},{"last_name":"Mazzuoccolo","full_name":"Mazzuoccolo, Guiseppe","first_name":"Guiseppe"},{"first_name":"Eckhard","id":"15548","last_name":"Steffen","full_name":"Steffen, Eckhard"}],"abstract":[{"lang":"eng","text":"There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such  measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures."}],"intvolume":"        25","status":"public","year":"2018","article_type":"original","publication":"The Electronic Journal of Combinatorics","date_updated":"2022-01-06T06:50:30Z","type":"journal_article","article_number":"P4.54","issue":"4","language":[{"iso":"eng"}]}