7 papers · 1 filter
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…