Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

2018

Journal or Book Title

The Electronic Journal of Combinatorics

Volume

25

Issue

3

First Page

P3.18

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 is published as P. DeOrsey J. Diemunsch, M. Ferrara, N. Graber, S. G. Hartke, S. Jahanbekam, B. Lidický, L. Nelsen, D. Stolee, E. Sullivan. "On the Strong Chromatic Index of Sparse Graphs." Electronic Journal of Combinatorics 25 (2018), #P3.18.

Creative Commons License

Creative Commons Attribution-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-No Derivative Works 4.0 License.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

Share

COinS