Maximal edge colorings of graphs
Combinatorics
2019-12-23 v1
Abstract
For a graph of order a maximal edge coloring is a proper edge coloring with colors such that adding any edge to in any color makes it improper. Meszka and Tyniec proved that for some values of the number of edges there are no graphs with a maximal edge coloring, while for some other values, they provided constructions of such graphs. However, for many values of the number of edges determining whether there exists any graph with a maximal edge coloring remained open. We give a complete solution of this problem.
Cite
@article{arxiv.1912.09538,
title = {Maximal edge colorings of graphs},
author = {Sebastian Babiński and Andrzej Grzesik},
journal= {arXiv preprint arXiv:1912.09538},
year = {2019}
}