Hitting time results for Maker-Breaker games

Sonny Ben-Shimon, Asaf Ferber, Dan Hefetz, Michael Krivelevich

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


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.

Original languageEnglish
Title of host publicationProceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011
Number of pages13
StatePublished - 2011
Externally publishedYes
Event22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011 - San Francisco, CA, United States
Duration: 23 Jan 201125 Jan 2011

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011
Country/TerritoryUnited States
CitySan Francisco, CA


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