Revisiting Semistrong Edge-Coloring of Graphs
Abstract
A matching in a graph is {\em semistrong} if every edge of has an endvertex of degree one in the subgraph induced by the vertices of . A {\em semistrong edge-coloring} of a graph is a proper edge-coloring in which every color class induces a semistrong matching. In this paper, we continue investigation of properties of semistrong edge-colorings initiated by Gy\'{a}rf\'{a}s and Hubenko ({Semistrong edge coloring of graphs}. \newblock {\em J. Graph Theory}, 49 (2005), 39--47). We establish tight upper bounds for general graphs and for graphs with maximum degree . We also present bounds about semistrong edge-coloring which follow from results regarding other, at first sight non-related, problems. We conclude the paper with several open problems.
Keywords
Cite
@article{arxiv.2208.13297,
title = {Revisiting Semistrong Edge-Coloring of Graphs},
author = {Borut Lužar and Martina Mockovčiaková and Roman Soták},
journal= {arXiv preprint arXiv:2208.13297},
year = {2023}
}