中文摘要：

对于完全图Kn和一个额外的顶点v,通过在v与Kn之间添加k条边所得出的图,记为Kn ∪K1,k.设G和H是任意的图,临界星图Ramsey数r＊（G,H）定义为最小的正整数kc,使得图KN-1∪ K1,k的任意红蓝2-边着色,或者存在单色的红色子图G,或者存在单色的蓝色子图H,这里N指的是Ramsey数r（G,H）.文中找到了r（Fn,mK2）的所有临界图,利用这些临界图得到了临界星图Ramsey数r＊（Fn,mK2）=m＋1,n＞m≥1,以及r＊（Fn,mK2）=2m,n≤m,这里Fn =K1 ＋nK2是扇形图.

英文摘要：

Let Kn LIK1,k be a graph obtained from K,, and an additional vertex v by joining v and k vertices of Kn. For graphs G and H, the star-critical Ramsey number r ＊ （G, H） is the smallest k such that every red/blue 2-edge coloring of Kn-xLIJ K1,k contains a red G or a blue H, where N is the Ramsey number r （ G, H）. Let Fn = K1 ＋ nK2 be a fangraph. All critical graphs of r （ Fn, mK2 ） are determined in this note. Also the star-critical Ramsey numbers r ＊ （Fn, inK2） = m＋1 for n〉m≥1 and r ＊ （Fn, mK2） =2m for n≤m are obtained by discussing these critical graphs.