### 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 K_{n}, 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 language | English (US) |
---|---|

Pages (from-to) | 569-584 |

Number of pages | 16 |

Journal | Journal of Graph Theory |

Volume | 18 |

Issue number | 6 |

DOIs | |

State | Published - 1994 |

### ASJC Scopus subject areas

- Geometry and Topology

## Fingerprint Dive into the research topics of 'Planar graph coloring with an uncooperative partner'. Together they form a unique fingerprint.

## Cite this

Kierstead, H., & Trotter, W. T. (1994). Planar graph coloring with an uncooperative partner.

*Journal of Graph Theory*,*18*(6), 569-584. https://doi.org/10.1002/jgt.3190180605