The Ramsey numbers of large trees versus wheels

Document Type: Research Paper

Authors

1 School of Economics and Management‎, ‎Southeast University‎, ‎Nanjing 210093‎, ‎P.R. China.

2 School of Management and Engineering‎, ‎Nanjing University‎, ‎Nanjing 210093‎, ‎P.R. China.

Abstract

For two given graphs $G_1$ and $G_2$, the Ramsey number $R(G_1,G_2)$ is the smallest integer n such that for any graph G of order n, either $G$ contains G1 or the complement of G contains $G_2$. Let Tn denote a tree of order n and Wm a wheel of order m+1. To the best of our knowledge, only $R(T_n,W_m)$ with small wheels are known. In this paper, we show that $R(T_n,W_m)=3n-2$ for odd m with $n>756m^{10}$.

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