On a star chromatic index of subcubic graphs

Abstract

A star edge-coloring of a graph is a proper edge-coloring without bichromatic paths and cycles of length four. We consider the list version of this coloring and prove that the list star chromatic index of every subcubic graph is at most 7, answering the question of Dvořák et al. in [Dvořák, Z., B. Mohar, and R. Šámal, Star chromatic index, J. Graph Theory 72 (2013), 313–326].