All i-th Ramsey numbers for stars

Abstract

A formula is presented that computes, for each positive integer i, the i-th Ramsey number of any collection of stars. In particular for the positive integers i, k, and n₁, n₂, . . ., n_k, it follows that ri(K(1,n₁),K(1,n₂),...,K(1,n_k)) = [[1 +j=1ςk(n_j - 1)] ÷ i] + θ where θ is either 0 or 1 and is completely determined as a function of n₁, n₂, . . ., n_k, and i. Also, given any collection of stars, it follows that r_i tends to 2 as i grows large. For such a collection, the least integer M is computed such that r_i = 2 whenever i ≥ M.