Ramsey games

This is a partly survey, partly new results paper about Ramsey games. Ramsey games belong to the wider class of positional games. In Section 1 we briefly recall the basic concepts and results of positional games in general, and apply them to the particular case of Ramsey games. For a more detailed introduction to the theory of positional games, including proofs we refer the reader to Beck [4] and [5].

[1]  József Beck,et al.  Van der waerden and ramsey type games , 1981, Comb..

[2]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[3]  Aleksandar Pekec,et al.  A Winning Strategy for the Ramsey Graph Game , 1995, Combinatorics, Probability and Computing.

[4]  Jeff B. Paris,et al.  More on the free subset problem , 1973 .

[5]  P. Erdös Some remarks on the theory of graphs , 1947 .

[6]  József Beck,et al.  Variations on a Game , 1982, J. Comb. Theory, Ser. A.

[7]  Keith Devlin Some weak versions of large cardinal axioms , 1973 .

[8]  Béla Bollobás,et al.  Random Graphs , 1985 .

[9]  J. Conway On Numbers and Games , 1976 .

[10]  A. Hajnal,et al.  Proof of a conjecture of B. Ruziewicz , 1961 .

[11]  P. Erdös,et al.  Combinatorial Theorems on Classifications of Subsets of a Given Set , 1952 .

[12]  József Beck Foundations of positional games , 1996 .

[13]  József Beck,et al.  Positional Games and the Second Moment Method , 2002, Comb..

[14]  Paul Erdös,et al.  On a Combinatorial Game , 1973, J. Comb. Theory A.

[15]  P. Erdös,et al.  Biased Positional Games , 1978 .