A linear upper bound in zero-sum Ramsey theory

Abstract

Let n, r and k be positive integers such that k|(nr). There exists a constant c(k,r) such that for fixed k and r and for every group A of order kR(Knr,A)≤n+c(k,r),where R(Knr,A) is the zero-sum Ramsey number introduced by Bialostocki and Dierker [1], and Knr is the complete r-uniform hypergraph on n-vertices.