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The Ramsey number $R(F,H)=\\min\\{r|\\; K_r\\rightarrow (F,H)\\}$. In this note, we consider redundant edges in Ramsey graphs, which are associate with critical Ramsey numbers. For an integer $k\\ge 1$, let ${\\mathbb G}=\\{G_k,G_{k+1},\\dots \\}$ be a class of graphs with $\\delta(G_n)\\ge 1$. 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