5 citations · 9 across the 11 of their papers we have counts for
11 papers
A counterexample to the - and the -Conjecture
Isaak H. Wolf
For two graphs and , a mapping is an -coloring of , if it is a proper edge-coloring and for every there exists a vertex $u \in V(H…
On the existence of factors intersecting sets of cycles in regular graphs
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo +3
A recent result by Kardoš, Máčajová and Zerafa [J. Comb. Theory, Ser. B. 160 (2023) 1--14] related to the famous Berge-Fulkerson conjecture implies that given an arbitrary set of o…
Some conjectures on -graphs and equivalences
Yulai Ma, Eckhard Steffen, Isaak H. Wolf +1
An -regular graph is an -graph, if every odd set of vertices is connected to its complement by at least edges. Seymour [On multicolourings of cubic graphs, and conjecture…
Cubic graphs with edges in exactly one perfect matching
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo +2
Petersen's seminal work in 1891 asserts that the edge-set of a cubic graph can be covered by distinct perfect matchings if and only if it is bridgeless. Actually, it is known that…
Fractional factors and component factors in graphs with isolated toughness smaller than 1
Isaak H. Wolf
Let be a simple graph and let be two integers with . We prove that for every if and only if has a $\{C_{2i+1},T…
Sets of -graphs that color all -graphs
Yulai Ma, Davide Mattiolo, Eckhard Steffen +1
An -regular graph is an -graph, if every odd set of vertices is connected to its complement by at least edges. Let and be -graphs. An -coloring of is a…
Rotation -graphs
Eckhard Steffen, Isaak H. Wolf
We study rotation -graphs and show that for every -graph of odd regularity there is a simple rotation -graph such that can be obtained form by a finite n…
Edge-connectivity and pairwise disjoint perfect matchings in regular graphs
Yulai Ma, Davide Mattiolo, Eckhard Steffen +1
For let be the maximum number such that every -edge-connected -graph has pairwise disjoint perfect matchings. There are only a few values o…
Bounds for the chromatic index of signed multigraphs
Eckhard Steffen, Isaak H. Wolf
The paper studies edge-coloring of signed multigraphs and extends classical Theorems of Shannon and König to signed multigraphs. We prove that the chromatic index of a signed multi…
Pairwise disjoint perfect matchings in -edge-connected -regular graphs
Yulai Ma, Davide Mattiolo, Eckhard Steffen +1
Thomassen [Problem 1 in Factorizing regular graphs, J. Combin. Theory Ser. B, 141 (2020), 343-351] asked whether every -edge-connected -regular graph of even order has …
Even factors in edge-chromatic-critical graphs with a small number of divalent vertices
Eckhard Steffen, Isaak H. Wolf
A finite simple connected graph with maximum degree is -critical if it has chromatic index and for every edge . Bej and the first auth…