扇形图与车轮图的Ramsey数

Ramsey Numbers of Fan versus Wheel

Ramsey数R(F,H)或r(F,H)是指给完全图KP的边红蓝着色时,至少有一个红色子图F,或者蓝色子图H的图的最小顶点个数P,即任意顶点个数为P的图或者包含F或者它的补图包含H。得到了结论有:若n是大于10的偶数,且Δ(G)≤n,|G|=2n+1,则或者G包含Wn,或者G的补图包含F2。

Ramsey numberR（F ,H） orr（F ,H） is defined as the minimum integer P such that any red -blue edge-coloring of KP contains a red F or a blue H .In other words ,it is the smallest integer P such that for any graphG of orderP ,eitherG containsF or the complement ofG containsH .It is determined the following result ：for evenn〉10 ,a graphG is of order2n＋1 with maximum degree no more than n , then eitherG contains aW n or its complement contains a F2 .