Clemens, DennisDennisClemensFerber, AsafAsafFerberKrivelevich, MichaelMichaelKrivelevichLiebenau, AnitaAnitaLiebenau2020-12-222020-12-222012-09-10Combinatorics Probability and Computing 6 (21): 897-915 (2012-11-01)http://hdl.handle.net/11420/8299In 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 ∼ 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. © 2012 Cambridge University Press.en1469-216320126897915Cambridge Univ. PressMathematikJournal Article10.1017/S0963548312000375Other