Odd graphs and its application on the strong edge coloring

Tao Wang, Xiaodan Zhao

Published 2014-12-29Version 1

A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index $\chiup_{s}'(G)$ of a graph $G$ is the minimum number of colors in a strong edge coloring of $G$. Let $\Delta \geq 4$ be an integer. In this note, we study the properties of the odd graphs, and show that every planar graph with maximum degree at most $\Delta$ and girth at least $10 \Delta - 4$ has a strong edge coloring using $2\Delta - 1$ colors.