Document Type

Article

Publication Date

July 2018

Publication Title

Electronic Journal of Combinatorics

Volume

25

Issue Number

3

First Page

3

Last Page

18

Keywords

Strong Edge Coloring, Strong Chromatic Index, Sparse Graphs

Disciplines

Discrete Mathematics and Combinatorics | Mathematics

Abstract

The strong chromatic index of a graph G, denoted χ′s(G), is the least number of colors needed to edge-color G so that edges at distance at most two receive distinct colors. The strong list chromatic index, denoted χ′s,ℓ(G), is the least integer k such that if arbitrary lists of size k are assigned to each edge then G can be edge-colored from those lists where edges at distance at most two receive distinct colors.We use the discharging method, the Combinatorial Nullstellensatz, and computation to show that if G is a subcubic planar graph with girth(G)≥41 then χ′s,ℓ(G)≤5, answering a question of Borodin and Ivanova [Precise upper bound for the strong edge chromatic number of sparse planar graphs, Discuss. Math. Graph Theory, 33(4), (2014) 759--770]. We further show that if G is a subcubic planar graph and girth(G)≥30, then χ′s(G)≤5, improving a bound from the same paper.Finally, if G is a planar graph with maximum degree at most four and girth(G)≥28, then χ′s(G)N≤7, improving a more general bound of Wang and Zhao from [Odd graphs and its applications to the strong edge coloring, Applied Mathematics and Computation, 325 (2018), 246-251] in this case.

Comments

This article was published in the Electronic Journal of Combinatorics, volume 25, issue 3, 2018. The article can also be found online at this link.
Copyright The Authors.

Download
COinS