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.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login