图的禁用子图和H—连通性

Forbidden Subgraphs and Hamiltonian-Connected Properties of Graphs

证明了如下结果：设Ｇ是３—连通图，如果Ｇ满足如下之一：（ｉ）｛Ｋ１，３，Ａ，Ｄ）－ｆｒｅｅ．（ｉｉ）｛Ｋ１，３，Ａ，Ｐ５｝－ｆｒｅｅ．（ｉｉｉ）｛Ｋ１，３，Ｉ｝－ｆｒｅｅ．（ｉｉｉｉ）｛Ｋ１，３，Ｚ３，Ｂ｝－ｆｒｅｅ．则Ｇ是Ｈ－连通的．

It was proved that:Theorem 1 Let G is a 3 - connected graph, {K1,3,A,D} -free, then G is Hamiltonian - connected.Theorem 2 Let G is a 3 - connected graph, {K1,3,A,P5 } -free, then G is Hamiltonian- connected.Theorem 3 Let G is a 3 - connected graph, {K1,3,I} -free, then G is Hamiltonian-connected.Theorem 4 Let G is a 3 - connected graph, {K1,3,Z3,B} -free, then G is Hamiltonian-connected.