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

Date and Time: Thursday, February 04, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Heidi Gebauer

Game Theoretic Ramsey Numbers

The Ramsey Number, R(k), is defined as the minimum N such that every 2-coloring of the edges of K_{N} (the complete graph on N vertices) yields a monochromatic k-clique. For 60 years it is known that 2^(k/2) < R(k) < 4^k, and it is a widely open problem to find significantly better bounds.

In this talk we consider a game theoretic variant of the Ramsey Numbers: Two players, called Maker and Breaker, alternately claim an edge of K_{N}. Maker's goal is to completely occupy a K_{k} and Breaker's goal is to prevent this. The game theoretic Ramsey Number R'(k) is defined as the minimum N such that Maker has a strategy to build a K_{k} in the game on K_{N}.

In contrast to the ordinary Ramsey Numbers, R'(k) has been determined precisely -- a result of Beck. We will sketch a new, weaker result about R'(k) and use it to solve some related open problems.

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