Ramsey number of multiple copies of stars.

Let G and H be simple graphs. The Ramsey number r (G , H) is the minimum integer N such that any red-blue-coloring of edges of K N contains either a red copy of G or a blue copy of H. Let m K 1 , t denote m vertex-disjoint copies of K 1 , t. A lower bound is that r (m K 1 , t , n K 1 , s) ≥ m (t + 1) + n − 1. Burr, Erdős and Spencer proved that this bound is indeed the Ramsey number r (m K 1 , t , n K 1 , s) for t = s = 3 , m ≥ 2 and m ≥ n. In this paper, we show that this bound is the Ramsey number r (m K 1 , t , n K 1 , s) for t ≥ s = 3 , m ≥ 2 and m ≥ n. We also show that this bound is the Ramsey number r (m K 1 , t , n K 1 , s) for s ≥ 4 , t > s (s − 1) 2 and m > n. [ABSTRACT FROM AUTHOR]