Cycle-Book Ramsey Numbers

Abstract

Let \(B_n = K(1,1,n)\) denote the \(n\)-book. In this paper we (i) calculate \(\lambda(C_5, B_n)\) for all \(n\),
(ii) prove that if \(m\) is an odd integer \(\geq 7\) and \(n \geq 4m – 13\) then \(r(C_m, B_n) = 2n + 3\),and (iii)
prove that if \(m \geq 2n + 2\) then \(r(C_m, B_n) = 2m – 1\).