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On the Strong Chromatic Index of Sparse Graphs
Electronic Journal of Combinatorics (2018)
  • Philip DeOrsey, Emory and Henry College
  • Jennifer Diemunsch, University of Colorado Denver
  • Michael Ferrara, University of Colorado Denver
  • Nathan Graber, University of Colorado Denver
  • Stephen G. Hartke, University of Colorado Denver
  • Sogol Jahanbekam, University of Colorado Denver
  • Bernard Lidicky, University of Colorado Denver
  • Luke L. Nelsen, University of Nebraska–Lincoln
  • Derrick Stolee, Iowa State University
  • Eric Sullivan, Iowa State University
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.
  • Strong Edge Coloring,
  • Strong Chromatic Index,
  • Sparse Graphs
Publication Date
July 27, 2018
Publisher Statement
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.
Citation Information
Philip DeOrsey, Jennifer Diemunsch, Michael Ferrara, Nathan Graber, et al.. "On the Strong Chromatic Index of Sparse Graphs" Electronic Journal of Combinatorics Vol. 25 Iss. 3 (2018) p. 3 - 18 ISSN: 1077-8926
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