A family of multigraphs with large palette index
Abstract
Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. The palette index of a multigraph is defined as the minimum number of distinct palettes occurring among the vertices, taken over all proper edge-colorings of the multigraph itself. In this framework, the palette multigraph of an edge-colored multigraph is defined in this paper and some of its properties are investigated. We show that these properties can be applied in a natural way in order to produce the first known family of multigraphs whose palette index is expressed in terms of the maximum degree by a quadratic polynomial. We also attempt an analysis of our result in connection with some related questions.
Keywords
Cite
@article{arxiv.1801.01336,
title = {A family of multigraphs with large palette index},
author = {Maddalena Avesani and Arrigo Bonisoli and Giuseppe Mazzuoccolo},
journal= {arXiv preprint arXiv:1801.01336},
year = {2018}
}
Comments
13 pages, 2 figures