Planarity, colorability, and minor games

Dan Hefetz, Michael Krivelevich, Miloš Stojaković, Tibor Szabó

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Let m and b be positive integers, and let F be a hypergraph. In an (m, b) Maker-Breaker game F two players, called Maker and Breaker, take turns selecting previously unclaimed vertices of F. Maker selects m vertices per move, and Breaker selects 6 vertices per move. The game ends when every vertex has been claimed by one of the players. Maker wins if he claims all of the vertices of some hyperedge of F; otherwise Breaker wins. An (m, b) Avoider-Enforcer game F is played in a similar way. The only difference is in the determination of the winner: Avoider loses if he claims all of the vertices of some hyperedge of F; otherwise Enforcer loses. In this paper we consider the Maker-Breaker and Avoider-Enforcer versions of the planarity game, the k-colorability game, and the Kt-minor game.

Original languageEnglish
Pages (from-to)194-212
Number of pages19
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2008
Externally publishedYes


  • Combinatorial games
  • Graph coloring
  • Graph minors
  • Planar graph


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