Building spanning trees quickly in maker-breaker games

Dennis Clemens, Asaf Ferber, Roman Glebov, Dan Hefetz, Anita Liebenau

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


For a tree T on n vertices, we study the Maker-Breaker game, played on the edge set of the complete graph on n vertices, which Maker wins as soon as the graph she builds contains a copy of T. We prove that if T has bounded maximum degree and n is sufficiently large, then Maker can win this game within n + 1 moves. Moreover, we prove that Maker can build almost every tree on n vertices in nâ'1 moves and provide nontrivial examples of families of trees which Maker cannot build in n â'1 moves.

Original languageEnglish
Pages (from-to)1683-1705
Number of pages23
JournalSIAM Journal on Discrete Mathematics
Issue number3
StatePublished - 2015
Externally publishedYes


  • Maker-Breaker games
  • Positional games
  • Spanning trees


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