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arXiv · 2208.13297

Revisiting Semistrong Edge-Coloring of Graphs

Borut Lužar·Martina Mockovčiaková·Roman Soták
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Abstract

A matching $M$ in a graph $G$ is {\em semistrong} if every edge of $M$ has an endvertex of degree one in the subgraph induced by the vertices of $M$. A {\em semistrong edge-coloring} of a graph $G$ 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 $3$. 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.

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Borut Lužar, Martina Mockovčiaková, Roman Soták. 2022-08-28. Revisiting Semistrong Edge-Coloring of Graphs. https://doi.org/10.1002/jgt.23059

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