Elsevier

Discrete Mathematics

Volume 309, Issues 23–24, 6 December 2009, Pages 6572-6584
Discrete Mathematics

A Brooks-type bound for squares of K4-minor-free graphs

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Abstract

Refining a bound by Lih, Wang and Zhu, we prove that if the square G2 of a K4-minor-free graph G with maximum degree Δ6 does not contain a complete subgraph on 32Δ+1 vertices, then G2 is 32Δ-colorable.

Keywords

Chromatic number
Vertex coloring
Brooks-type bound
Square of a graph
Series–parallel graph

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