A Note On Some Ramsey Numbers \(R(C_{p}, C_{q}, C_{r})\)

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.