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Injective edge-coloring of graphs with given maximum degree

2020/10/01 by Alexandr Kostochka, Kostochka, Alexandr, André Raspaud +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2010.00429

openalex publication_date 2020/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A coloring of edges of a graph G is injective if for any two distinct edges e1 and e2, the colors of e1 and e2 are distinct if they are at distance 1 in G or in a common triangle. Naturally, the injective chromatic index of G, χ'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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