List star edge coloring of generalized Halin graphs

Abstract

The star chromatic index χ st (G) of a graph G is the smallest integer k for which G has a proper k-edge coloring without bichromatic paths or cycles of length four. In this paper, we prove that if H is a Halin graph with maximum degree ∆ ≥ 14, then χ st (H) ≤ 3 2 ∆ . This bound is tight.