Homogeneous Edge-Colorings of Graphs
Combinatorics
2012-03-21 v1
Abstract
Let G = (V, E) be a multigraph without loops and for any x {\in}V let E(x) be the set of edges of G incident to x. A homogeneous edge-coloring of G is an assignment of an integer m >= 2 and a coloring c:E {\to} S of the edges of Gsuchthat|S| = mandforanyx{\in}V,if|E(x)| = mqx+rx with0 <= rx <m, there exists a partition of E(x) in rx color classes of cardinality qx + 1 and other m-rx color classes of cardinality qx. The homogeneous chromatic index \c{hi}(G) is the least m for which there exists such a coloring. We determine \c{hi}(G) in the case that G is a complete multigraph, a tree or a complete bipartite multigraph.
Keywords
Cite
@article{arxiv.1203.4531,
title = {Homogeneous Edge-Colorings of Graphs},
author = {Paola Bonacini and Maria Grazia Cinquegrani and Lucia Marino},
journal= {arXiv preprint arXiv:1203.4531},
year = {2012}
}