极小(C_4,K_5;11)-平面图

Minimal(C_4,K_5;11)-P-graphs

若n阶平面图G的任一子图都不与H_1同构,且G的任一子图都不与H_2同构,则G称为(H_1,H_2;n)-平面图;平面Ramsey数指不存在(H_1,H_2;n)-平面图的最小n。本文利用对称性及反证等方法,得到了所有的极小(C_4,K_5;11)-平面图,有助于证明平面Ramsey数。

An （H1 ,H2;n）-P-graph is a graph with order n, which does not contain a subgraph isomorphic to H1, and its complement has no subgraph isomorphic to H2. Planar Ramsey number is the minimum order of graph ,which does not con- tain （H1 ,H2 ;n）-P-graph. In this paper,all the minimal （C4 ,K5 ;11 ）-P-graphs are given by the methods of disproof and symmetry.