2012/01/31 by Vahan V. Mkrtchyan · 1 citation
Computer Science · Mathematics · #cs.DM #math.CO
published as Australasian Journal of Combinatorics 56, (2013), 145-151 · 6 pages, 2 figures, + the comments of the referees are taken into account+ Sylvester coloring conjecture is introduced+ a result related with this conjectures is proved
arxiv created 2012/07/24 · arxiv updated 2013/05/22
If G and H are two cubic graphs, then we write H\prec G, if G admits a proper edge-coloring f with edges of H, such that for each vertex x of G, there is a vertex y of H with f(∂G(x))=∂H(y). Let P and S be the Petersen graph and the Sylvester graph, respectively. In this paper, we introduce the Sylvester coloring conjecture. Moreover, we show that if G is a connected bridgeless cubic graph with G\prec P, then G=P. Finally, if G is a connected cubic graph with G\prec S, then G=S.