Fast embedding of spanning trees in biased Maker-Breaker games

Asaf Ferber, Dan Hefetz, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Given a tree T=(V, E) on n vertices, we consider the (1:q) Maker-Breaker tree embedding game T n. The board of this game is the edge set of the complete graph on n vertices. Maker wins Tn if and only if she 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 n ε, Maker has a winning strategy for the (1:q) game Tn, for every q≤n α. Moreover, we prove that Maker can win this game within n+o(n) moves which is clearly asymptotically optimal.

Original languageEnglish
Pages (from-to)1086-1099
Number of pages14
JournalEuropean Journal of Combinatorics
Volume33
Issue number6
DOIs
StatePublished - Aug 2012
Externally publishedYes

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