Game list colouring of graphs

M. Borowiecki, E. Sidorowicz, Zs Tuza

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider the two-player game defined as follows. Let (G, L) be a graph G with a list assignment L on its vertices. The two players, Alice and Bob, play alternately on G, Alice having the first move. Alice's goal is to provide an L-colouring of G and Bob's goal is to prevent her from doing so. A move consists in choosing an uncoloured vertex v and assigning it a colour from the set L(v). Adjacent vertices of the same colour must not occur. This game will be called game list colouring. The game choice number of G, denoted by chg(G), is defined as the least k such that Alice has a winning strategy for any k-list assignment of G. We characterize the class of graphs with chg(G) < 2 and determine the game choice number for some classes of graphs.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalElectronic Journal of Combinatorics
Volume14
Issue number1 R
Publication statusPublished - Mar 22 2007

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Borowiecki, M., Sidorowicz, E., & Tuza, Z. (2007). Game list colouring of graphs. Electronic Journal of Combinatorics, 14(1 R), 1-11.