Positional games and the second moment method
The aim of the present paper is to study the fair Maker-Breaker graph Ramsey game. It is shown that the Maker has a winning strategy in the game if certain conditions are satisfied which is exacly 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.
scientific article; zbMATH DE number 1822335