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.
Keywords
Cite
@article{arxiv.1605.02588,
title = {A Vizing-like theorem for union vertex-distinguishing edge coloring},
author = {Nicolas Bousquet and Antoine Dailly and Eric Duchene and Hamamache Kheddouci and Aline Parreau},
journal= {arXiv preprint arXiv:1605.02588},
year = {2026}
}