k连通图可缩边导出子图的连通性

The Connectivity of Induced Subgraph by all Contractible Edges in K-Connected Graph

引进S1 3边形的概念 .证明了 ,对于k(k =3或 4)连通图G ,若G无S1 3边形 ,则 <EC(G) >是 2连通的 ;另外也得到 ,设G是k(k≥ 2 )连通图 ,若对G的任一断片F ,有｜F｜ >[k/2 ]+ 1 ,则 <EC(G) >是 2连通的 .从而改进并推广了N .Dean的结论 .

If G is 3 or 4 connected praph without S 1 triangle.Then <E C(G)> is 2 connected;In addition,If G is k(k≥3) connected graph whose each fragment satisies that |F|≥+1,Then <E C(G)> is 2 connected.