Planar graph coloring with an uncooperative partner

Henry Kierstead, W. T. Trotter

Research output: Contribution to journalArticle

88 Citations (Scopus)

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

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Game Chromatic number
Graph Coloring
Planar graph
Graph in graph theory
Genus

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Planar graph coloring with an uncooperative partner. / Kierstead, Henry; Trotter, W. T.

In: Journal of Graph Theory, Vol. 18, No. 6, 1994, p. 569-584.

Research output: Contribution to journalArticle

Kierstead, Henry ; Trotter, W. T. / Planar graph coloring with an uncooperative partner. In: Journal of Graph Theory. 1994 ; Vol. 18, No. 6. pp. 569-584.
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