### 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 |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

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

**Planar graph coloring with an uncooperative partner.** / Kierstead, Henry; Trotter, W. T.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 18, no. 6, pp. 569-584. https://doi.org/10.1002/jgt.3190180605

}

TY - JOUR

T1 - Planar graph coloring with an uncooperative partner

AU - Kierstead, Henry

AU - Trotter, W. T.

PY - 1994

Y1 - 1994

N2 - 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 Kn, 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.

AB - 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 Kn, 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.

UR - http://www.scopus.com/inward/record.url?scp=84987487282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987487282&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190180605

DO - 10.1002/jgt.3190180605

M3 - Article

AN - SCOPUS:84987487282

VL - 18

SP - 569

EP - 584

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 6

ER -