www.elsevier.com/locate/ejc The Ramsey numbers of stars versus wheels

For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest positive integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Sn denote a star of order n and Wm a wheel of order m+1. This paper shows that R(Sn, W6) = 2n+1 for n ≥ 3 and R(Sn, Wm) = 3n − 2 for m odd and n ≥ m − 1 ≥ 2