Playing to retain the advantage

Noga Alon, Dan Hefetz, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Let P be a monotone increasing graph property, let G = (V, E) be a graph, and let q be a positive integer. In this paper, we study the (1: q) Maker-Breaker game, played on the edges of G, in which Maker's goal is to build a graph that satisfies the property P. It is clear that in order for Maker to have a chance of winning, G itself must satisfy P. We prove that if G satisfies P in some strong sense, that is, if one has to delete sufficiently many edges from G in order to obtain a graph that does not satisfy P, then Maker has a winning strategy for this game. We also consider a different notion of satisfying some property in a strong sense, which is motivated by a problem of Duffus, Łuczak and Rödl [6].

Original languageEnglish
Pages (from-to)481-491
Number of pages11
JournalCombinatorics Probability and Computing
Issue number4
StatePublished - Jul 2010
Externally publishedYes


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