A Note On the Ramsey Numbers \(R(C_{4}, B_{n})\)

The Ramsey number \( R(C_4, B_n) \) is the smallest positive integer \( m \) such that for every graph \( F \) of order \( m \), either \( F \) contains \( C_4 \) (a quadrilateral) or \( \overline{F} \) contains \( B_n \) (a book graph \( K_2 + \overline{K_n} \) of order \( n+2 \)). Previously, we computed \( R(C_4, B_n) = n+9 \) for \( 8 \leq n \leq 12 \). In this continuing work, we find that \( R(C_4, B_{13}) = 22 \) and surprisingly \( R(C_4, B_{14}) = 24 \), showing that their values are not incremented by one, as one might have suspected. The results are based on computer algorithms.