[1]周小跃.泛圈图的一个新的充分条件[J].东南大学学报(自然科学版),2000,30(6):114-118.[doi:10.3969/j.issn.1001-0505.2000.06.024]
 Zhou Xiaoyue.A New Sufficient Condition for Pancyclic Graphs[J].Journal of Southeast University (Natural Science Edition),2000,30(6):114-118.[doi:10.3969/j.issn.1001-0505.2000.06.024]
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泛圈图的一个新的充分条件()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
30
期数:
2000年第6期
页码:
114-118
栏目:
数学、物理学、力学
出版日期:
2000-11-20

文章信息/Info

Title:
A New Sufficient Condition for Pancyclic Graphs
作者:
周小跃
南京建筑工程学院,南京 210009
Author(s):
Zhou Xiaoyue
Nanjing Architectural and Civil Engineering Institute, Nanjing 210009
关键词:
泛圈性 Hamilton图 充分条件
Keywords:
pancyclicity Hamilton graph sufficient condition
分类号:
O157.5
DOI:
10.3969/j.issn.1001-0505.2000.06.024
摘要:
设G是一个阶为n的2-连通简单图,αv表示G中包含点v的最大独立集的点数,对任意uv∈/ E,设Tuv=V\(N(u)∪N(v)),αuv=min{αuv}.本文证明了:如果对于任一对不相邻点u,v,|N(u)∩N(v)|≥min{αuv-1,|Tuv|},则除一些特殊图外,对于G的任一点x和任意整数k(4≤k≤n),G包含长度为k且包含点x的圈.
Abstract:
Let G be a 2-connected simple graph of order n and αv denote the order of the largest independent set containing the vertex v in G. For any uv∈/ E, let Tuv=V\(N(u)∪N(v)),αuv=min{αuv}. This paper proves that if for any non-adjacent vertices u,v, |N(u)∩N(v)|≥min{αuv-1,|Tuv|}, then there exists cycle G of length k such that G contains vertex x for any vertex x and any k(4≤k≤n),except some special graphs.

参考文献/References:

[1] Bondy J A,Murty U S R.Graph theory with applications.London:The Macmillan Press,1976
[2] Aldred R E Z,Holton D A,Zhang K M.A degree characterisation of pancyclicity.Discrete Math,1994,127:23~29
[3] Bauer D,Schmeichel E.Hamiltonian degree conditions which imply a graph is pancyclic.J Combin Theory,1990,B48:111~146
[4] Bedrossian P,Chen G,Schelp R H.A generalization of Fan’s condition for Hamiltonicity,pancyclicity and hamiltonian connectedness.Discrete Math,1993(115):39~50

备注/Memo

备注/Memo:
第一作者:女,1958年生, 讲师.
更新日期/Last Update: 2000-11-20