2012/03/20 by Paola Bonacini, Bonacini, Paola, Maria Grazia Cinquegrani +3
Computer Science · Mathematics · Neuroscience · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Nuclear Receptors and Signaling #math.CO
paper · pdf · doi:10.48550/arxiv.1203.4531
arxiv created 2012/03/20 · arxiv updated 2012/03/21
Let G = (V, E) be a multigraph without loops and for any x ∈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 → S of the edges of Gsuchthat|S| = mandforanyx∈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 \chi(G) is the least m for which there exists such a coloring. We determine \chi(G) in the case that G is a complete multigraph, a tree or a complete bipartite multigraph.