www.elsevier.com/locate/disc The Ramsey numbers of paths versus wheels �

For two givengraphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Pn denote a path of order n and Wm a wheel of order m + 1. Inthis paper, we show that R(Pn,Wm) = 2n − 1 for m evenand n�m − 1�3 andR(Pn,Wm) = 3n − 2 for m odd and n�m − 1�2. © 2004 Elsevier B.V. All rights reserved