Note on list star edge-coloring of subcubic graphs

TL;DR

This paper proves that the list star chromatic index of any subcubic graph is at most 7, resolving a previously open question about list star edge-colorings.

Contribution

It establishes an upper bound of 7 for the list star chromatic index of all subcubic graphs, advancing understanding of star edge-colorings.

Findings

List star chromatic index of subcubic graphs is at most 7

Answers an open question in graph coloring literature

Provides a bound for a specific class of graphs.

Abstract

{\emph A star edge-coloring} of a graph is a proper edge-coloring without bichromatic paths and cycles of length four. In this paper, 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 Dvo\v{r}\'{a}k et al. (Star chromatic index, J. Graph Theory 72 (2013), 313--326).