For graphs F, G and H, let \(F\rightarrow (G,H)\) signify that any red/blue edge coloring of F contains either a red G or a blue H. The Ramsey number R(G, H) is defined as the minimum r such that \(K_r\rightarrow (G,H)\), and the star-critical Ramsey number \(R_{{\mathbb {S}}}(G,H)\) is defined as the maximum n such that \(K_r\setminus K_{1,n}\rightarrow (G,H)\), where \(r=R(G,H)\). We shall determine \(R_{{\mathbb {S}}}(K_2+G,K_1+nH)\) to be \(v(H)n-\delta (H)-1\) for all large n.

中文翻译：

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广义粉丝的明星临界拉姆齐数

对于图F、G和H，让\(F\rightarrow (G,H)\)表示F 的任何红色/蓝色边缘着色包含红色G或蓝色H。拉姆齐数R ( G ,  H ) 被定义为最小r使得\(K_r\rightarrow (G,H)\)和星临界拉姆齐数\(R_{{\mathbb {S}}}( G,H)\)定义为最大n使得\(K_r\setminus K_{1,n}\rightarrow (G,H)\)，其中\(r=R(G,H)\)。我们将确定\(R_{{\mathbb {S}}}(K_2+G,K_1+nH)\)是\(v(H)n-\delta (H)-1\)对于所有大n。