Ramsey set numbers in balanced complete multipartite graphs
One natural extension of classical Ramsey numbers to multipartite graphs is to consider 2-
colorings of the complete multipartite graph consisting of n parts, each of size k, denoted K
n× k. We may then ask for the minimum integer n such that K n× k→{G, H} for two given
graphs G and H. We study this number for the the cases when C and H are paths or cycles
and show some general bounds and relations to classical Ramsey theory.
colorings of the complete multipartite graph consisting of n parts, each of size k, denoted K
n× k. We may then ask for the minimum integer n such that K n× k→{G, H} for two given
graphs G and H. We study this number for the the cases when C and H are paths or cycles
and show some general bounds and relations to classical Ramsey theory.
Abstract
One natural extension of classical Ramsey numbers to multipartite graphs is to consider 2-colorings of the complete multipartite graph consisting of n parts, each of size k, denoted K n× k. We may then ask for the minimum integer n such that K n× k→{G, H} for two given graphs G and H. We study this number for the the cases when C and H are paths or cycles and show some general bounds and relations to classical Ramsey theory.
digitalcommons.georgiasouthern.edu