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arXiv · 2010.00429

Injective edge-coloring of graphs with given maximum degree

Alexandr Kostochka·André Raspaud·Jingwei Xu
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Abstract

A coloring of edges of a graph $G$ is injective if for any two distinct edges $e_1$ and $e_2$, the colors of $e_1$ and $e_2$ are distinct if they are at distance $1$ in $G$ or in a common triangle. Naturally, the injective chromatic index of $G$, $\chi'_{inj}(G)$, is the minimum number of colors needed for an injective edge-coloring of $G$. We study how large can be the injective chromatic index of $G$ in terms of maximum degree of $G$ when we have restrictions on girth and/or chromatic number of $G$. We also compare our bounds with analogous bounds on the strong chromatic index.

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Alexandr Kostochka, André Raspaud, Jingwei Xu. 2020-10-01. Injective edge-coloring of graphs with given maximum degree. https://arxiv.org/abs/2010.00429

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