For two given graphs $G$ and $H$, the extit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we shall study the Ramsey number $R(T_n,W_{m})$ for a star-like tree $T_n$ with $n$ vertices and a wheel $W_m$ with $m+1$ vertices and $m$ odd. We show that the Ramsey number $R(S_{n},W_{m})=3n-2 $ for $ngeq 2m-4, mgeq 5$ and $m$ odd, where $S_n$ denotes the star on $n$ vertices. We conjecture that the Ramsey number is the same for general trees on $n$ vertices, and support this conjecture by proving it for a number of star-like trees.
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机译：对于两个给定的图形$ G $和$ H $， textit {拉姆西数} $ R（G，H）$是最小的正整数$ N $，因此对于每个定额$ N $的图形$ F $，以下项持有：$ F $包含$ G $作为子图，或者$ F $的补数包含$ H $作为子图。在本文中，我们将研究具有$ n $顶点的星形树$ T_n $和具有$ m + 1 $顶点和$$的轮子$ W_m $的Ramsey数$ R（T_n，W_ {m}）$ m $奇数。我们显示Ramsey数$ R（S_ {n}，W_ {m}）= 3n-2 $为$ n geq 2m-4，m geq 5 $和$ m $奇数，其中$ S_n $表示在$ n $个顶点上加星号。我们推测Ramsey数对于$ n $顶点上的一般树是相同的，并通过证明许多星形树来支持这种猜想。
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