On the Ramsey numbers r(G,nH) and r(nG,nH) when n is large (Q1090340)

Let G and H be graphs. The Ramsey number \(r(G,H)\) is the smallest number p so that, if the edges of the complete graph on p vertices are colored with orange and blue, then either there is a subgraph isomorphic to G with all of its edges colored orange or a subgraph isomorphic to H with all of its edges colored blue. This paper is concerned with graphs of the form nG, i.e. the graph consisting of n disjoint copies of G. Several results are proved including: Theorem 5.3: If k and h are fixed and n is sufficiently large, then: \[ r(nK_ k,nK_ h)=(k+h-1)n+r(K_{k- 1},K_{h-1})-2. \]