Ramsey numbers of fans and large books (Q2121798)

Summary: For graphs \(G\) and \(H\), the Ramsey number \(R(G,H)\) is the minimum integer \(N\) such that any red/blue edge coloring of \(K_N\) contains either a red \(G\) or a blue \(H\). Let \(G+H\) be the graph obtained from vertex disjoint \(G\) and \(H\) by adding new edges connecting \(G\) and \(H\) completely, \(F_m=K_1+mK_2\) and \(B_p(n)=K_p+nK_1\). It is shown \(R(F_m,B_p(n))=2(n+p-1)+1\) for fixed \(m, p\) and large \(n\).