On Pattern Ramsey Numbers of Graphs

Abstract

A color pattern is a graph whose edges are partitioned into color classes. A family F of color patterns is a Ramsey family if there is some integer N such that every edge-coloring of KN has a copy of some pattern in F. The smallest such N is the (pattern) Ramsey number R(F) of F. The classical Canonical Ramsey Theorem of Erdos and Rado [4] yields an easy characterization of the Ramsey families of color patterns. In this paper we determine R(F) for all families consisting of equipartitioned stars, and we prove that ** when F consists of a monochromatic star of size s and a polychromatic triangle.