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

Xingchao Deng, Qingye Yao, Yanbing Zhang and Xudong Cui

Applied Mathematics and Computation, 2020, vol. 384, issue C

Abstract: 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.

Keywords: Star chromatic index; Diameter; Outerplanar graph; Maximal outerplanar graph (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320303179

DOI: 10.1016/j.amc.2020.125353

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