Interval edge-colorings of cubic graphs [article]

Petros A. Petrosyan
2011 arXiv   pre-print
An edge-coloring of a multigraph G with colors 1,2,...,t is called an interval t-coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In this paper we prove that if G is a connected cubic multigraph (a connected cubic graph) that admits an interval t-coloring, then t≤ |V(G)| +1 (t≤ |V(G)|), where V(G) is the set of vertices of G. Moreover, if G is a connected cubic graph, G≠ K_4, and G has an interval t-coloring,
more » ... t≤ |V(G)| -1. We also show that these upper bounds are sharp. Finally, we prove that if G is a bipartite subcubic multigraph, then G has an interval edge-coloring with no more than four colors.
arXiv:1110.1161v1 fatcat:tpbwlrrvnrcz5cc4aucpycwnia