List injective edge-coloring of subcubic graphs

Abstract

An edge-coloring 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 2 in G or in a common triangle. The injective chromatic index of G, χinj′(G), is the minimum number of colors needed for an injective edge-coloring of G. In this paper, we consider the list version of the injective edge-coloring and prove that the list-injective chromatic index of every subcubic graph is at most 7, which generalizes the recent result of Kostochka et al. (2021).