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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 - Optimisation Combinatoire
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.
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Submitted on : Monday, July 17, 2017 - 1:36:43 PM
Last modification on : Monday, March 21, 2022 - 11:22:02 AM
Long-term archiving on: : Saturday, January 27, 2018 - 3:42:07 AM


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Nicolas Bousquet, Antoine Dailly, Eric Duchene, Hamamache Kheddouci, Aline Parreau. A Vizing-like theorem for union vertex-distinguishing edge coloring. Discrete Applied Mathematics, Elsevier, 2017, 232, pp.88-98. ⟨10.1016/j.dam.2017.07.002⟩. ⟨hal-01313088v2⟩



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