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Fast Strategies In Maker–Breaker Games Played on Random Boards

  • DENNIS CLEMENS (a1), ASAF FERBER (a2), MICHAEL KRIVELEVICH (a2) and ANITA LIEBENAU (a1)

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) ≥ 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.

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Fast Strategies In Maker–Breaker Games Played on Random Boards

  • DENNIS CLEMENS (a1), ASAF FERBER (a2), MICHAEL KRIVELEVICH (a2) and ANITA LIEBENAU (a1)

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