Adapted game colouring of graphs

Henry Kierstead, Chung Ying Yang, Daqing Yang, Xuding Zhu

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Suppose G=(V, E) is a graph and F is a colouring of its edges (not necessarily proper) that uses the colour set X. In an adapted colouring game, Alice and Bob alternately colour uncoloured vertices of G with colours from X. A partial colouring c of the vertices of G is legal if there is no edge e=xy such that c(x)=c(y)=F(e). In the process of the game, each partial colouring must be legal. If eventually all the vertices of G are coloured, then Alice wins the game. Otherwise, Bob wins the game. The adapted game chromatic number of a graph G, denoted by χ adg(G), is the minimum number of colours needed to ensure that for any edge colouring F of G, Alice has a winning strategy for the game. This paper studies the adapted game chromatic number of various classes of graphs. We prove that the maximum adapted game chromatic number of trees is 3, the maximum adapted game chromatic number of outerplanar graphs is 5, the adapted game chromatic number of partial k-trees is at most 2k+1, and the adapted game chromatic number of planar graphs is at most 11.

Original languageEnglish (US)
Pages (from-to)435-445
Number of pages11
JournalEuropean Journal of Combinatorics
Volume33
Issue number4
DOIs
StatePublished - May 1 2012

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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