Fast embedding of spanning trees in biased Maker-Breaker games

Dan Hefetz, Asaf Ferber, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review

Abstract

Given a tree T=(V, E) on n vertices, we consider the (1:q) Maker-Breaker tree embedding game Tn. The board of this game is the edge set of the complete graph on n vertices. Maker wins Tn if and only if he is able to claim all edges of a copy of T. We prove that there exist real numbers α, ε>0 such that, for sufficiently large n and for every tree T on n vertices with maximum degree at most nε, Maker has a winning strategy for the (1:q) game Tn, for every q≤nα. Moreover, we prove that Maker can win this game within n+o(n) moves which is clearly asymptotically optimal.

Original languageEnglish
Pages (from-to)331-336
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume38
DOIs
StatePublished - 1 Dec 2011

Keywords

  • Embedding spanning trees
  • Hamilton connected
  • Maker-Breaker games

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