Coloring, List Coloring, and Painting Squares of Graphs (and Other Related Problems)

A strong edge coloring of a graph G is a proper coloring of edges in G such that any two edges of distance at most 2 are colored with distinct colors. The strong chromatic index χs′(G) is the smallest integer l such that G admits a strong edge coloring using l colors. A K4(t)-minor free graph is a graph that does not contain K4(t) as a contraction subgraph, where K4(t) is obtained from a K4 by subdividing edges exactly t−4 times. The paper shows that every K4(t)-minor free graph with maximum degree Δ(G) has χs′(G)≤(t−1)Δ(G) for t∈{5,6,7} which generalizes some known results on K4-minor free graphs by Batenburg, Joannis de Verclos, Kang, Pirot in 2022 and Wang, Wang, and Wang in 2018. These upper bounds are sharp.

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Coloring, List Coloring, and Painting Squares of Graphs (and Other Related Problems)

Abstract: We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse classes of graphs.

Cited by 2 publications

References 156 publications

Square coloring of planar graphs with maximum degree at most five

Square coloring of planar graphs with maximum degree at most five

Strong Edge Coloring of K4(t)-Minor Free Graphs

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