A note on the Ramsey number of even wheels versus stars

Sh. Haghi; H. R. Maimani

paper

A note on the Ramsey number of even wheels versus stars

arXiv:1510.08488

Abstract

For two graphs $G_{1}$ and $G_{2}$ the Ramsey number $R (G_{1}, G_{2})$ is the smallest integer $N$ , such that for any graph on $N$ vertices either $G$ contains $G_{1}$ or $G$ contains $G_{2}$ . Let $S_{n}$ be a star of order $n$ and $W_{m}$ be a wheel of order $m + 1$ . In this paper, it is shown that $R (W_{n}, S_{n}) \leq 5 n /2 - 1$ , where $n \geq 6$ is even. It was proven a theorem which implies that $R (W_{n}, S_{n}) \geq 5 n /2 - 2$ , where $n \geq 6$ is even. Therefore we conclude that $R (W_{n}, S_{n}) = 5 n /2 - 2$ or $5 n /2 - 1$ , for $n \geq 6$ and even.