Class Ramsey numbers of odd cycles in many colors

摘要

Let C2m+1={C3,C5,⋯,C2m+1} be the family of odd cycles of length at most 2m+1. The Class Ramsey number Rk(C2m+1) is defined as the smallest integer N such that any k-edge-coloring of KN contains at least a monochromatic odd cycle in C2m+1. In this note, we study the behaviour of Rk(C2m+1) for large k.