Fast strategies in makera-breaker games played on random boards

Dennis Clemens*, Asaf Ferber, Michael Krivelevich, Anita Liebenau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we analyse classical Maker-Breaker games played on the edge set of a sparse random board G n,p. We consider the Hamiltonicity game, the perfect matching game and the k-connectivity game. We prove that for p(n) â‰1 polylog(n)/n the board G ∼ n,p is typically such that Maker can win these games asymptotically as fast as possible, i.e., within n+o(n), n/2+o(n) and kn/2+o(n) moves respectively.

Original languageEnglish
Pages (from-to)897-915
Number of pages19
JournalCombinatorics Probability and Computing
Volume21
Issue number6
DOIs
StatePublished - Nov 2012

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