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Journal articles
A Vizing-like theorem for union vertex-distinguishing edge coloring
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.
https://hal.archives-ouvertes.fr/hal-01313088
Contributor : Antoine Dailly <>
Submitted on : Monday, July 17, 2017 - 1:36:43 PM
Last modification on : Thursday, November 19, 2020 - 1:12:04 PM
Long-term archiving on: : Saturday, January 27, 2018 - 3:42:07 AM
Contributor : Antoine Dailly <>
Submitted on : Monday, July 17, 2017 - 1:36:43 PM
Last modification on : Thursday, November 19, 2020 - 1:12:04 PM
Long-term archiving on: : Saturday, January 27, 2018 - 3:42:07 AM
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