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 \(R(C_5, W_6) = 13, \quad R(C_5, W_7) = 15, \quad R(C_5, W_8) = 17\),\(R(C_6, W_6) = 11, \quad R(C_6, W_7) = 16, \quad R(C_6, W_8) = 13\),\(R(C_7, W_6) = 13 \quad \text{and} \quad R(C_7, W_8) = 17\).