TY - JOUR

T1 - Efficient Winning Strategies in Random-Turn Maker–Breaker Games

AU - Ferber, Asaf

AU - Krivelevich, Michael

AU - Kronenberg, Gal

N1 - Publisher Copyright:
© 2016 Wiley Periodicals, Inc.

PY - 2017/6

Y1 - 2017/6

N2 - We consider random-turn positional games, introduced by Peres, Schramm, Sheffield, and Wilson in 2007. A p-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is p). We analyze the random-turn version of several classical Maker–Breaker games such as the game Box (introduced by Chvátal and Erdős in 1987), the Hamilton cycle game and the k-vertex-connectivity game (both played on the edge set of Kn). for each of these games we provide each of the players with a (randomized) efficient strategy that typically ensures his win in the asymptotic order of the minimum value of p for which he typically wins the game, assuming optimal strategies of both players.

AB - We consider random-turn positional games, introduced by Peres, Schramm, Sheffield, and Wilson in 2007. A p-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is p). We analyze the random-turn version of several classical Maker–Breaker games such as the game Box (introduced by Chvátal and Erdős in 1987), the Hamilton cycle game and the k-vertex-connectivity game (both played on the edge set of Kn). for each of these games we provide each of the players with a (randomized) efficient strategy that typically ensures his win in the asymptotic order of the minimum value of p for which he typically wins the game, assuming optimal strategies of both players.

KW - Maker-Breaker games

KW - positional games

KW - random graphs

UR - http://www.scopus.com/inward/record.url?scp=84995982197&partnerID=8YFLogxK

U2 - 10.1002/jgt.22072

DO - 10.1002/jgt.22072

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AN - SCOPUS:84995982197

SN - 0364-9024

VL - 85

SP - 446

EP - 465

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 2

ER -