三角连通［4,2］-图的完全圈可扩性

J4 ›› 2010, Vol. 23 ›› Issue (6): 13-15.

三角连通［4,2］-图的完全圈可扩性

王磊, 王江鲁

山东师范大学数学科学学院，山东济南 250014

收稿日期:2010-06-10 出版日期:2010-12-20 发布日期:2010-12-20

Fully Cycle Extendability of a Triangularly Connected［4,2］-Graphs

WANG Lei, WANG Jiang-Lu

School of Mathematics,Shandong Normal University,Jinan 250014,China

Received:2010-06-10 Online:2010-12-20 Published:2010-12-20

摘要/Abstract

摘要：

如果G的任意s个点的导出子图中至少含有t条边，则称图G为［s,t］图.本文证明了:若G是无孤立点的三角连通［4,2］-图,则G或者是完全圈可扩的或者同构于F.其中图F有与图K3∨K2同构的导出子图.

关键词: ［s, t］-图, 完全圈可扩, 三角连通

Abstract:

A graph G is a ［s,t］-graph, if the included subgraphs of its any s vertices have at least t edges.This paper proves that G is either fullcycle extendable or isomorphic to graph F if G is a triangularly connected［4,2］graph without any isolated vertex.Graph F has an induced subgraph isomorphic to K3∨K2.

Key words: [s,t］-graphs;full cycle extendability;triangular connection

中图分类号:

O157.5

王磊, 王江鲁. 三角连通［4,2］-图的完全圈可扩性[J]. J4, 2010, 23(6): 13-15.

WANG Lei, WANG Jiang-Lu. Fully Cycle Extendability of a Triangularly Connected［4,2］-Graphs[J]. J4, 2010, 23(6): 13-15.

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