4 papers
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…
On the existence of factors intersecting sets of cycles in regular graphs
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo +3
A recent result by KardoÅ¡, MáÄajová and Zerafa [J. Comb. Theory, Ser. B. 160 (2023) 1--14] related to the famous Berge-Fulkerson conjecture implies that given an arbitrary set…
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…
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…