@article{12971,
author = {Jin, Ligang and Steffen, Eckhard},
journal = {J. of Combinatorics, to appear},
title = {{Unions of 1-factors in r-graphs and overfull graphs}},
year = {2019},
}
@unpublished{13114,
abstract = {Many basic properties in Tutte's flow theory for unsigned graphs do not have
their counterparts for signed graphs. However, signed graphs without long
barbells in many ways behave like unsigned graphs from the point view of flows.
In this paper, we study whether some basic properties in Tutte's flow theory
remain valid for this family of signed graphs. Specifically let $(G,\sigma)$ be
a flow-admissible signed graph without long barbells. We show that it admits a
nowhere-zero $6$-flow and that it admits a nowhere-zero modulo $k$-flow if and
only if it admits a nowhere-zero integer $k$-flow for each integer $k\geq 3$
and $k \not = 4$. We also show that each nowhere-zero positive integer $k$-flow
of $(G,\sigma)$ can be expressed as the sum of some $2$-flows. For general
graphs, we show that every nowhere-zero $\frac{p}{q}$-flow can be normalized in
such a way, that each flow value is a multiple of $\frac{1}{2q}$. As a
consequence we prove the equality of the integer flow number and the ceiling of
the circular flow number for flow-admissible signed graphs without long
barbells.},
author = {Lu, You and Luo, Rong and Schubert, Michael and Steffen, Eckhard and Zhang, Cun-Quan},
booktitle = {arXiv:1908.11004},
title = {{Flows on signed graphs without long barbells}},
year = {2019},
}
@unpublished{15445,
abstract = {We construct highly edge-connected $r$-regular graph which do not contain
$r-2$ pairwise disjoint perfect matchings. The results partially answer a
question stated by Thomassen [Factorizing regular graphs, J. Comb. Theory Ser.
B (2019), https://doi.org/10.1016/j.jctb.2019.05.002 (article in press)].},
author = {Mattiolo, Davide and Steffen, Eckhard},
booktitle = {arXiv:1912.09704},
title = {{Highly edge-connected regular graphs without large factorizable subgraphs}},
year = {2019},
}
@unpublished{13445,
abstract = {The paper surveys some concepts of signed graph colorings.},
author = {Steffen, Eckhard and Vogel, Alexander},
booktitle = {arXiv:1909.09381},
title = {{Concepts of signed graph coloring}},
year = {2019},
}
@unpublished{12970,
abstract = {The paper studies component-factors of graphs which can be characterized in
terms of their fractional matching number. These results are used to prove that
every edge-chromatic critical graph has a $[1,2]$-factor. Furthermore,
fractional matchings of edge-chromatic critical graphs are studied and some
questions are related to Vizing's conjectures on the independence number and
2-factors of edge-chromatic critical graphs.},
author = {Klopp, Antje and Steffen, Eckhard},
booktitle = {arXiv:1903.12385},
title = {{Fractional matchings and component-factors of (edge-chromatic critical) graphs}},
year = {2019},
}
@article{10142,
author = {Steffen, Eckhard},
journal = {Australasian Journal of Combinatorics},
number = {1},
pages = {153--160},
title = {{Approximating Vizing’s independence number conjecture}},
volume = {71},
year = {2018},
}
@article{10130,
author = {Rollová, Edita and Schubert, Michael and Steffen, Eckhard},
journal = {Electronic Journal of Combinatorics},
number = {2},
title = {{Signed Graphs with Two Negative Edges }},
volume = {25},
year = {2018},
}
@article{10129,
abstract = {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.},
author = {Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard},
journal = {The Electronic Journal of Combinatorics},
keyword = {Cubic graph, Tait coloring, Snark, Boole coloring, Berge's conjecture, Tutte's 5-flow conjecture},
number = {4},
title = {{Measures of Edge-Uncolorability of Cubic Graphs}},
volume = {25},
year = {2018},
}
@article{10132,
author = {Jin, Ligang and Mazzuoccolo, Giuseppe and Steffen, Eckhard},
issn = {1234-3099},
journal = {Discussiones Mathematicae Graph Theory},
pages = {165--175},
title = {{Cores, joins and the Fano-flow conjectures}},
doi = {10.7151/dmgt.1999},
volume = {38},
year = {2018},
}
@book{10146,
editor = {Maier, Günter W. and Engels, Gregor and Steffen, Eckhard},
publisher = {Springer Berlin Heidelberg},
title = {{Handbuch Gestaltung digitaler und vernetzter Arbeitswelten}},
year = {2017},
}
@inbook{10147,
author = {Simon, Dagmar and Steffen, Eckhard},
booktitle = {Handbuch Gestaltung digitaler und vernetzter Arbeitswelten,},
editor = {Maier, Günter W. and Engels, Gregor and Steffen, Eckhard},
pages = {1--12},
publisher = {Springer Berlin Heidelberg},
title = {{Digitale Zukunft: ein inter- und transdisziplinäres Thema}},
year = {2017},
}
@inbook{10143,
author = {Engels, Gregor and Maier, Günter W. and Ötting, Sonja K. and Steffen, Eckhard and Teetz, Alexander},
booktitle = {Zukunft der Arbeit – Eine praxsnahe Betrachtung},
editor = {Wischmann, S. and Hartmann, E. A,},
pages = { 221--231 },
publisher = {Springer Vieweg},
title = {{Gerechtigkeit in flexiblen Arbeits- und Managementprozessen}},
year = {2017},
}
@article{10155,
author = {Mazzuoccolo, Guiseppe and Steffen, Eckhard},
journal = {J. Graph Theory},
pages = {363 – 371 },
title = {{Nowhere-zero 5-flows on cubic graphs with oddness 4}},
volume = {85},
year = {2017},
}
@article{10156,
author = {Bej, Saptarshi and Steffen, Eckhard},
journal = {Lecture Notes of Seminario Interdisciplinare di Matematica},
pages = {37--48},
title = {{Factors of edge-chromatic critical graphs: a brief survey and some equivalences}},
volume = {14},
year = {2017},
}
@article{10157,
author = {Jin, Ligang and Steffen, Eckhard},
journal = {J. Graph Theory},
pages = {109 -- 120 },
title = {{Petersen cores and the oddness of cubic graphs}},
volume = {84},
year = {2017},
}
@article{10158,
author = {Jin, Ligang and Kang, Yingli and Steffen, Eckhard},
journal = {Electronic Journal of Combinatorics},
number = {3},
title = {{Face-degree bounds for planar critical graphs}},
volume = {23},
year = {2016},
}
@article{10160,
author = {Jin, Ligang and Kang, Yingli and Steffen, Eckhard},
journal = {Discrete Applied Mathematics},
pages = {200–202},
title = {{Remarks on planar critical graphs}},
volume = {200},
year = {2016},
}
@article{10161,
author = {Jin, Ligang and Kang, Yingli and Steffen, Eckhard},
journal = {European J. Combinatorics},
pages = {234--243},
title = {{Choosability in signed planar graphs}},
volume = {52},
year = {2016},
}
@article{10159,
author = {Kang, Yingli and Steffen, Eckhard},
journal = {Discrete Mathematics },
pages = {234--243},
title = {{The chromatic spectrum of signed graphs}},
volume = {339},
year = {2016},
}
@article{10165,
author = {Steffen, Eckhard},
journal = {J. Graph Theory},
number = {3},
pages = {195 – 206},
title = {{1-factor-and cycle covers of cubic graphs}},
volume = {78},
year = {2015},
}