TY - GEN

T1 - Hitting time results for Maker-Breaker games

AU - Ben-Shimon, Sonny

AU - Ferber, Asaf

AU - Hefetz, Dan

AU - Krivelevich, Michael

PY - 2011

Y1 - 2011

N2 - We analyze classical Maker-Breaker games played on the edge set of a randomly generated graph G. We consider the random graph process and analyze, for each of the properties "being spanning k-vertex-connected" , "admitting a perfect matching", and "being Hamiltonian", the first time when Maker starts having a winning strategy for building a graph possessing the target property (the so called hitting time). We prove that typically it happens precisely at the time the random graph process first reaches minimum degree 2k, 2 and 4, respectively, which is clearly optimal. The latter two statements settle conjectures of Stojaković and Szabó. We also consider a general-purpose game, the expander game. which is a main ingredient of our proofs and might be of an independent interest.

AB - We analyze classical Maker-Breaker games played on the edge set of a randomly generated graph G. We consider the random graph process and analyze, for each of the properties "being spanning k-vertex-connected" , "admitting a perfect matching", and "being Hamiltonian", the first time when Maker starts having a winning strategy for building a graph possessing the target property (the so called hitting time). We prove that typically it happens precisely at the time the random graph process first reaches minimum degree 2k, 2 and 4, respectively, which is clearly optimal. The latter two statements settle conjectures of Stojaković and Szabó. We also consider a general-purpose game, the expander game. which is a main ingredient of our proofs and might be of an independent interest.

UR - http://www.scopus.com/inward/record.url?scp=79955727358&partnerID=8YFLogxK

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AN - SCOPUS:79955727358

SN - 9780898719932

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 900

EP - 912

BT - Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

T2 - 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

Y2 - 23 January 2011 through 25 January 2011

ER -