The Ramsey numbers of paths versus wheels

@article{Chen2005TheRN,
  title={The Ramsey numbers of paths versus wheels},
  author={Yaojun Chen and Yunqing Zhang and Kemin Zhang},
  journal={Discrete Mathematics},
  year={2005},
  volume={290},
  pages={85-87}
}
For two given graphs G1 andG2, the Ramsey number R(G1, G2) is the smallest integer nsuch that for any graphG of ordern, eitherG containsG1 or the complement of G containsG2. LetPn denote a path of ordern andWm a wheel of orderm + 1. In this paper, we show that R(Pn, Wm) = 2n − 1 formeven andn m − 1 3 andR(Pn, Wm) = 3n − 2 formodd andn m − 1 2. © 2004 Elsevier B.V. All rights reserved.