## Abstract

Using a fixed set of colors C, Ann and Ben color the edges of a graph G so that no monochromatic cycle may appear. Ann wins if all edges of G have been colored, while Ben wins if completing a coloring is not possible. The minimum size of C for which Ann has a winning strategy is called the game arboricity of G, denoted by A_{g} (G). We prove that A_{g} (G) ≤ 3 k for any graph G of arboricity k, and that there are graphs such that A_{g} (G) ≥ 2 k - 2. The upper bound is achieved by a suitable version of the activation strategy, used earlier for the vertex coloring game. We also provide two other strategies based on induction and acyclic colorings.

Original language | English (US) |
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Pages (from-to) | 1388-1393 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 8 |

DOIs | |

State | Published - Apr 28 2008 |

## Keywords

- Acyclic coloring
- Arboricity
- Degenerate graph
- Game arboricity

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics