Positional Games and the Second Moment Method

Dedicated to the memory of Paul Erdős

We study the fair Maker–Breaker graph Ramsey game MB(n;q). The board is , the players alternately occupy one edge a move, and Maker wants a clique of his own. We show that Maker has a winning strategy in MB(n;q) if , which is exactly the clique number of the random graph on n vertices with edge-probability 1/2. Due to an old theorem of Erdős and Selfridge this is best possible apart from an additive constant.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Received March 28, 2000

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Beck, J. Positional Games and the Second Moment Method. Combinatorica 22, 169–216 (2002). https://doi.org/10.1007/s004930200009

Download citation

  • AMS Subject Classification (2000) Classes:  91A24