Revisiting semistrong edge‐coloring of graphs

Abstract

A matching in a graph is semistrong if every edge of has an endvertex of degree one in the subgraph induced by the vertices of . A 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 Gyárfás and Hubenko. We establish tight upper bounds for general graphs and for graphs with maximum degree 3. We also present bounds about semistrong edge‐coloring which follow from results regarding other, at first sight nonrelated, problems. We conclude the paper with several open problems.