On Ramsey numbers for large disjoint unions of graphs (Q1104338)

Let \({\mathcal G}\) denote a fixed finite set of connected graphs. This paper contains results which, in principle, enable one to evaluate the Ramsey number r(G,H) when G and H are sufficiently large disjoint unions of graphs taken from \({\mathcal G}\). Using this result the author computes: \[ r(mK_ k,nK_ h)=(k-1)m+hn+r(K_{k-1},K_{h-1})-2 \] when m and n are sufficiently large with \(m\leq n\).