2-连通[4,2]-图中的圈

The cycle in 2-connected -graphs

如果图G中任意s个点的导出子图至少含有t条边,则称图G为[s,t]-图.设是2-连通[4,2]-图,C是G中满足|V(C)|<|V(G)|的任一圈,则或者G中有(|C|+1)-圈,或者G同构于K2,3,K1,1,3,F1,F2,F3,F4,F5之一.

A graph G is called [ s, t ]-graph, if there are at least t edges in every induced subgraph of s vertices. Let G be a 2- connected [4,2]-graph, C is a cycle in G, which satisfies the condition ｜ V（ C） ｜ 〈 ｜ V（ G） ｜, then either G has a （ ｜C｜＋ 1）- cycle, or G is isomorphic to one of K2,3, K1,1,3, F1 , F2, F3, F4, F5.