We determine the exact value of the $2$-color Ramsey number of a connected $4$-clique matching $\mathscr{C}(nK_4)$ which is a set of connected graphs containing $n$ disjoint $K_4$. That is, we show that $R_2(\mathscr{C}(nK_4)) = 13n-3$ for any positive integer $n \geq 3$. The result is an extension of the result by (Roberts, 2017) which gave that result when $n\geq 18$. We also show that the result still holds when $n=2$ provided that $R_2(2K_4) \leq 23$.

翻译：我们确定了连通4-团匹配$\mathscr{C}(nK_4)$的2-色拉姆齐数的精确值，其中$\mathscr{C}(nK_4)$是一组包含$n$个不相交$K_4$的连通图。即，我们证明了对于任意正整数$n \geq 3$，有$R_2(\mathscr{C}(nK_4)) = 13n-3$。这一结果是对(Roberts, 2017)结论的推广，该文献给出了$n\geq 18$时的结果。我们还证明了当$n=2$且满足$R_2(2K_4) \leq 23$时，该结论仍然成立。