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A Vizing-like theorem for union vertex-distinguishing edge coloring

By Nicolas Bousquet, Antoine Dailly, Eric Duchene, Hamamache Kheddouci and Aline Parreau

Abstract

International audienceWe introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the problem of finding a coloring with the minimum number of colors where every vertex receives a distinct label. Finding such a coloring generalizes several other well-known problems of vertex-distinguishing colorings in graphs.We show that for any graph (without connected component reduced to an edge or a single vertex), the minimum number of colors for which such a coloring exists can only take 3possible values depending on the order of the graph. Moreover, we provide the exact value for paths, cycles and complete binary trees

Topics: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Publisher: 'Elsevier BV'
Year: 2017
DOI identifier: 10.1016/j.dam.2017.07.002
OAI identifier: oai:HAL:hal-01313088v2
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