A Note On Some Ramsey Numbers $R(C_p,C_q,C_r)$

Abstract

The Ramsey number $R(C_p,C_q,C_r)$ is the smallest positive integer $m$ such that no matter how one colors the edges of the $K_m$ in red, white, and blue, there must be a red $C_p$, a white $C_q$, or a blue $C_r$. In this work, we verified some known $R(C_p,C_q,C_r)$ values and computed some new $R(C_p,C_q,C_r)$ values. The results are based on computer algorithms.