TY - JOUR
AU - Jin, Ligang
AU - Steffen, Eckhard
ID - 12971
JF - J. of Combinatorics, to appear
TI - Unions of 1-factors in r-graphs and overfull graphs
ER -
TY - GEN
AB - 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.
AU - Lu, You
AU - Luo, Rong
AU - Schubert, Michael
AU - Steffen, Eckhard
AU - Zhang, Cun-Quan
ID - 13114
T2 - arXiv:1908.11004
TI - Flows on signed graphs without long barbells
ER -
TY - GEN
AB - 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)].
AU - Mattiolo, Davide
AU - Steffen, Eckhard
ID - 15445
T2 - arXiv:1912.09704
TI - Highly edge-connected regular graphs without large factorizable subgraphs
ER -
TY - GEN
AB - The paper surveys some concepts of signed graph colorings.
AU - Steffen, Eckhard
AU - Vogel, Alexander
ID - 13445
T2 - arXiv:1909.09381
TI - Concepts of signed graph coloring
ER -
TY - GEN
AB - 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.
AU - Klopp, Antje
AU - Steffen, Eckhard
ID - 12970
T2 - arXiv:1903.12385
TI - Fractional matchings and component-factors of (edge-chromatic critical) graphs
ER -
TY - JOUR
AU - Steffen, Eckhard
ID - 10142
IS - 1
JF - Australasian Journal of Combinatorics
TI - Approximating Vizing’s independence number conjecture
VL - 71
ER -
TY - JOUR
AU - Rollová, Edita
AU - Schubert, Michael
AU - Steffen, Eckhard
ID - 10130
IS - 2
JF - Electronic Journal of Combinatorics
TI - Signed Graphs with Two Negative Edges
VL - 25
ER -
TY - JOUR
AB - 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.
AU - Fiol, M. A.
AU - Mazzuoccolo, Guiseppe
AU - Steffen, Eckhard
ID - 10129
IS - 4
JF - The Electronic Journal of Combinatorics
KW - Cubic graph
KW - Tait coloring
KW - Snark
KW - Boole coloring
KW - Berge's conjecture
KW - Tutte's 5-flow conjecture
TI - Measures of Edge-Uncolorability of Cubic Graphs
VL - 25
ER -
TY - JOUR
AU - Jin, Ligang
AU - Mazzuoccolo, Giuseppe
AU - Steffen, Eckhard
ID - 10132
JF - Discussiones Mathematicae Graph Theory
SN - 1234-3099
TI - Cores, joins and the Fano-flow conjectures
VL - 38
ER -
TY - BOOK
ED - Maier, Günter W.
ED - Engels, Gregor
ED - Steffen, Eckhard
ID - 10146
TI - Handbuch Gestaltung digitaler und vernetzter Arbeitswelten
ER -
TY - CHAP
AU - Simon, Dagmar
AU - Steffen, Eckhard
ED - Maier, Günter W.
ED - Engels, Gregor
ED - Steffen, Eckhard
ID - 10147
T2 - Handbuch Gestaltung digitaler und vernetzter Arbeitswelten,
TI - Digitale Zukunft: ein inter- und transdisziplinäres Thema
ER -
TY - CHAP
AU - Engels, Gregor
AU - Maier, Günter W.
AU - Ötting, Sonja K.
AU - Steffen, Eckhard
AU - Teetz, Alexander
ED - Wischmann, S.
ED - Hartmann, E. A,
ID - 10143
T2 - Zukunft der Arbeit – Eine praxsnahe Betrachtung
TI - Gerechtigkeit in flexiblen Arbeits- und Managementprozessen
ER -
TY - JOUR
AU - Mazzuoccolo, Guiseppe
AU - Steffen, Eckhard
ID - 10155
JF - J. Graph Theory
TI - Nowhere-zero 5-flows on cubic graphs with oddness 4
VL - 85
ER -
TY - JOUR
AU - Bej, Saptarshi
AU - Steffen, Eckhard
ID - 10156
JF - Lecture Notes of Seminario Interdisciplinare di Matematica
TI - Factors of edge-chromatic critical graphs: a brief survey and some equivalences
VL - 14
ER -
TY - JOUR
AU - Jin, Ligang
AU - Steffen, Eckhard
ID - 10157
JF - J. Graph Theory
TI - Petersen cores and the oddness of cubic graphs
VL - 84
ER -
TY - JOUR
AU - Jin, Ligang
AU - Kang, Yingli
AU - Steffen, Eckhard
ID - 10158
IS - 3
JF - Electronic Journal of Combinatorics
TI - Face-degree bounds for planar critical graphs
VL - 23
ER -
TY - JOUR
AU - Jin, Ligang
AU - Kang, Yingli
AU - Steffen, Eckhard
ID - 10160
JF - Discrete Applied Mathematics
TI - Remarks on planar critical graphs
VL - 200
ER -
TY - JOUR
AU - Jin, Ligang
AU - Kang, Yingli
AU - Steffen, Eckhard
ID - 10161
JF - European J. Combinatorics
TI - Choosability in signed planar graphs
VL - 52
ER -
TY - JOUR
AU - Kang, Yingli
AU - Steffen, Eckhard
ID - 10159
JF - Discrete Mathematics
TI - The chromatic spectrum of signed graphs
VL - 339
ER -
TY - JOUR
AU - Steffen, Eckhard
ID - 10165
IS - 3
JF - J. Graph Theory
TI - 1-factor-and cycle covers of cubic graphs
VL - 78
ER -