We determine the size Ramsey number \(\hat{r}(P_3,H)\) for all graphs H of order five. Thus, for the first time a complete column of the table of all size Ramsey numbers \(\hat{r}(G,H)\) where \(p(G) \le 5\) and \(p(H) = 5\) is obtained. In contrast, for the (vertex) Ramsey number r(G, H) all such exact results but two are already known. Furthermore, our results grant the opportunity to compare \(\hat{r}(P_3,H)\) with the recently published corresponding restricted size Ramsey number \(\hat{r}^{*}(P_3,H)\) for all connected graphs H of order five. In the course of our investigations we derive some new general results on the size Ramsey number \(\hat{r}(P_3,H)\), e.g. for some classes of almost complete graphs H. Additionally, minding that \(P_3 = K_{1,2}\) is a star, we consider \(\hat{r}(K_{1,m},K_{1,n_1} \cup K_{1,n_2})\).

我们确定所有五阶图H的大小 Ramsey 数\(\hat{r}(P_3,H)\)。因此，对于所有大小的拉姆齐数\(\hat{r}(G,H)\)其中\(p(G) \le 5\)和\(p(H) = 5\)得到。相比之下，对于（顶点）拉姆齐数r ( G ,  H ) 所有这样的精确结果，但两个是已知的。此外，我们的结果提供了将\(\hat{r}(P_3,H)\)与最近发布的相应限制大小的拉姆齐数\(\hat{r}^{*}(P_3,H)\) 进行比较的机会对于所有连通图H五阶。在我们的调查过程中，我们得出了一些关于大小 Ramsey 数\(\hat{r}(P_3,H)\) 的新的一般结果，例如对于几乎完整的图H 的某些类别。此外，考虑到\(P_3 = K_{1,2}\)是一颗恒星，我们考虑\(\hat{r}(K_{1,m},K_{1,n_1} \cup K_{1,n_2 })\)。