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 $\ge 7$ and $n\ge 4m–13$ then $r(C_m,B_n)=2n+3$,and (iii)
prove that if $m\ge 2n+2$ then $r(C_m,B_n)=2m–1$.