### 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 ch_{g}(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 ch_{g}(G) < 2 and determine the game choice number for some classes of graphs.

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Electronic Journal of Combinatorics |

Volume | 14 |

Issue number | 1 R |

Publication status | Published - 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

*Electronic Journal of Combinatorics*,

*14*(1 R), 1-11.