Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, November 05, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Dan Hefetz

Playing to retain the advantage

Let P be a monotone decreasing graph property, let G=(V,E) be a graph, and let q be a positive integer. In this talk, I will discuss the (1 : q) Maker-Breaker game, played on the edges of G, in which Maker's goal is to build a graph that does not satisfy the property P. It is clear that in order for Maker to have a chance of winning, G must not satisfy P. It turns out that if G is far from satisfying P, that is, if one has to delete many edges from G in order to obtain a graph that satisfies P, then Maker has a winning strategy for this game. I will also discuss a different notion of being far from satisfying some property, which is motivated by a problem of Duffus, Łuczak and Rödl.

Based on joint work with N. Alon and M. Krivelevich .

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