Computation of Ramsey Numbers $R(C_m,W_n)$

Abstract

For given finite simple graphs $F$ and $G$, the Ramsey number $R(F,G)$ is the minimum positive integer $n$ such that for every graph $H$ of order $n$, either $H$ contains $F$ or the complement of $H$ contains $G$. In this note, with the help of computer, we get that $R(C_5,W_6)=13,R(C_5,W_7)=15,R(C_5,W_8)=17$,$R(C_6,W_6)=11,R(C_6,W_7)=16,R(C_6,W_8)=13$,$R(C_7,W_6)=13\text{and}R(C_7,W_8)=17$.