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

Nicolas Bousquet 1 Antoine Dailly 2 Eric Duchene 2 Hamamache Kheddouci 2 Aline Parreau 2
1 G-SCOP_OC - OC
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
2 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : We 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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01313088
Contributeur : Antoine Dailly <>
Soumis le : lundi 17 juillet 2017 - 13:36:43
Dernière modification le : mercredi 19 juillet 2017 - 12:34:02

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  • HAL Id : hal-01313088, version 2
  • ARXIV : 1605.02588

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Nicolas Bousquet, Antoine Dailly, Eric Duchene, Hamamache Kheddouci, Aline Parreau. A Vizing-like theorem for union vertex-distinguishing edge coloring. 2017. 〈hal-01313088v2〉

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