Ramsey graphs and block designs

Abstract

Symmetric (ν, κ, λ)-block designs admitting polarity maps are shown to be closely related to certain Ramsey numbers for bipartite graphs. In particular, if there exists a (ν, κ, λ)-difference set in an abelian group of order ν, then the Ramsey number R( K 2, λ+1 , K 1, ν− k+1 ) is either 1 + ν or 2 + ν.