Planar graph coloring with an uncooperative partner

Henry Kierstead, W. T. Trotter

Research output: Contribution to journalArticle

90 Scopus citations

Abstract

We show that the game chromatic number of a planar graph is at most 33. More generally, there exists a function f: ℕ → ℕ so that for each n ∈ ℕ, if a graph does not contain a homeomorph of Kn, then its game chromatic number is at most f(n). In particular, the game chromatic number of a graph is bounded in terms of its genus. Our proof is motivated by the concept of p‐arrangeability, which was first introduced by Guantao and Schelp in a Ramsey theoretic setting.

Original languageEnglish (US)
Pages (from-to)569-584
Number of pages16
JournalJournal of Graph Theory
Volume18
Issue number6
DOIs
StatePublished - 1994

ASJC Scopus subject areas

  • Geometry and Topology

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