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Given graphs $ F_1, F_2$ and $G$, we say that $G$ is Ramsey for $(F_1,F_2)$and we write $G\rightarrow(F_1, F_2)$, if for every edge coloring of $G$ by redand blue, there is either a red copy of $F_1$ or a blue copy of $F_2$ in $G$.The size Ramsey number $\hat{r}(F_1, F_2)$ is defined as the minimum number ofedges of a graph $G$ such that $G\rightarrow(F_1, F_2)$. This paper providesthe exact value of $\hat{r}(F_1, F_2)$ for many pairs $(F_1, F_2)$ of starforests, giving a partial solution to a conjecture of Burr et al.(Ramsey-minimal graphs for multiple copies, Indagationes Mathematicae, 81(2)(1978), 187-195).

On a Conjecture of Erd\H os on Size Ramsey Number of Star Forests