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Fast Strategies In Maker–Breaker Games Played on Random Boards

Published online by Cambridge University Press:  10 September 2012

DENNIS CLEMENS ,
ASAF FERBER ,
MICHAEL KRIVELEVICH  and
ANITA LIEBENAU
DENNIS CLEMENS
Affiliation:
Department of Mathematics and Computer Science, Freie Universität Berlin, Germany (e-mail: d.clemens@fu-berlin.de, liebenau@math.fu-berlin.de)
ASAF FERBER
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel (e-mail: ferberas@post.tau.ac.il, krivelev@post.tau.ac.il)
MICHAEL KRIVELEVICH
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel (e-mail: ferberas@post.tau.ac.il, krivelev@post.tau.ac.il)
ANITA LIEBENAU
Affiliation:
Department of Mathematics and Computer Science, Freie Universität Berlin, Germany (e-mail: d.clemens@fu-berlin.de, liebenau@math.fu-berlin.de)
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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.

Keywords

Primary 05C8005C5791A4391A46
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 6 , November 2012 , pp. 897 - 915
Copyright
Copyright © Cambridge University Press 2012

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