International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 609-612

A linear upper bound in zero-sum Ramsey theory

Yair Caro

Department of Mathematics, School of Education, University of Haifa - ORANIM, Tivon 36-910, Israel

Received 19 May 1992

Copyright © 1994 Yair Caro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.