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arXiv · 1203.4531

Homogeneous Edge-Colorings of Graphs

Paola Bonacini·Maria Grazia Cinquegrani·Lucia Marino
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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.

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Paola Bonacini, Maria Grazia Cinquegrani, Lucia Marino. 2012-03-20. Homogeneous Edge-Colorings of Graphs. https://arxiv.org/abs/1203.4531

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