A note on a conjecture of star chromatic index for outerplanar graphs

摘要

A star edge coloring of a graph G is a proper edge coloring of G without bichromatic paths or cycles of length four. The star chromatic index, χst′(G), of G is the minimum number k for which G has a star edge coloring by k colors. In [2], L. Bezegova´ et al. conjectured that χst′(G)≤⌊3Δ2⌋+1 when G is an outerplanar graph with maximum degree Δ ≥ 3. In this paper we obtained that χst′(G)≤Δ+6 when G is an 2-connected outerplanar graph with diameter 2 or 3. If G is an 2-connected outerplanar graph with maximum degree 5, then χst′(G)≤9.