The game of arboricity

T. Bartnicki, J. A. Grytczuk, Henry Kierstead

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 Ag (G). We prove that Ag (G) ≤ 3 k for any graph G of arboricity k, and that there are graphs such that Ag (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 languageEnglish (US)
Pages (from-to)1388-1393
Number of pages6
JournalDiscrete Mathematics
Volume308
Issue number8
DOIs
StatePublished - Apr 28 2008

Keywords

  • Acyclic coloring
  • Arboricity
  • Degenerate graph
  • Game arboricity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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