## Abstract

Nešetřil and Sopena introduced a concept of oriented game chromatic number and developed a general technique for bounding this parameter. In this paper, we combine their technique with concepts introduced by several authors in a series of papers on game chromatic number to show that for every positive integer k, there exists an integer t so that if C is a topologically closed class of graphs and C does not contain a complete graph on k vertices, then whenever G is an orientation of a graph from C, the oriented game chromatic number of G is at most t. In particular, oriented planar graphs have bounded oriented game chromatic number. This answers a question raised by Nešetřil and Sopena. We also answer a second question raised by Nesetfil and Sopena by constructing a family of oriented graphs for which oriented game chromatic number is bounded but extended Go number is not.

Original language | English (US) |
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Pages (from-to) | XXXXI-XXXXII |

Journal | Electronic Journal of Combinatorics |

Volume | 8 |

Issue number | 2 |

State | Published - Dec 1 2001 |

## Keywords

- Chromatic number
- Competitive algorithm
- Oriented graph

## ASJC Scopus subject areas

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