TT-′free图的最长圈

The longest cycle in TT′-free graphs

本文提出了两类新的禁用子图T和T′.一个图G称为TT-′free图,若G中不含同构于T或T′的导出子图,它是比无爪图更广的一个图类.G的一个圈C称为控制圈(简记为D-圈),若E(G-C)=Φ.本文证明了:顶点数不小于3的连通、局部连通TT-′free图G最长圈为D-圈,且G是局部泛圈的.

We introduced the forbidden subgraphs T and T＇ that never mentioned before. A graph G is called TT＇-free graph if there are no induced subgraphs in G isomorphic to the subgraph T or T. And the TT＇-free graphs is a class of graphs larger than the claw-free graphs. In this paper, we proved if G is connected, local connected TT＇-free graph of order larger than 3, then the longest cycle of G is a dominating cycle, and G is subpancyclic.