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A Simple Proof for the Bondy Theorem on pancyclic Graphs

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Chinese Quarterly Journal of Mathematics 2002年第2期17卷 14-15页

作者：赵克文韩烽李大超琼州大学数学系海南师范学院数学系海南海口571100 海南师范学院数学系

A new short proof is given for the Bondy Theorem on pancyclic graphs.

关键词： Bondy Theorem pancyclic cycles

An Implicit Degree Ore-condition for pancyclicity of Graphs

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Acta Mathematica Sinica,English Series 2013年第9期29卷 1773-1780页

作者： Hao LI Jun Qing CAI L.R.I UMR 8623 CNRS and Universit Paris-Sud 11 F-91405 Orsay France Institute for Interdisciplinary Research Jianghan University School of Management Qufu Normal University

In 1989, Zhu, Li and Deng introduced the definition of implicit degree of a vertex v in a graph G, denoted by id（v）. In this paper, we prove that if G is a 2-connected graph of order n such that id（u）＋ id（v） ≥ n for each pair of nonadjacent vertices u and v in G, then G is pancyclic unless G is bipartite, or else n = 4r, r ≥ 2 and G is isomorphic to F4r .

关键词： Implicit degree Hamilton cycle pancyclic graph

A Bilevel Decision Method for the Multiobjective Problem with 0-1 Variables

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Journal of Southeast University(English Edition) 1996年第1期12卷 113-118页

作者： Guohua(Department of Mathematics, Southeast University, Nanjing 210018)

It is shown that if G is a 2 connected graph on n≥10 vertices such that d(x)+d(y)+d(z)≥3n/2-2 for every triple of vertices x,y,z with min {d(x,y),d(y,z),d(x,z)}=2 , then G is pancyclic or ... 详细信息

关键词： degree sum pancyclic graph vertex distance

A Generalized Neighborhood Union Condition for pancyclicity

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Journal of Southeast University(English Edition) 1997年第1期13卷 109-113页

作者：林文松

Let G be a 2 connected simple graph with order n (n≥6) and minimum degree δ . This paper proves that if for any independent set of three vertices { u,v,w} V(G ) there always exist x and y∈{... 详细信息

关键词： cycle pancyclic pancyclic graph

On Some Cycles in Wenger Graphs

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 492-502页

作者： Ye WANG Felix LAZEBNIK Andrew THOMASON College of Mathematical Sciences Harbin Engineering UniversityHarbin 150001China Department of Mathematical Sciences University of DelawareNewark.DE 19716U.S.A. DPMMS Centre for Mathematical SciencesWilberforce RoadCambridgeUK

Let p be a prime,q be a power of p,and let Fq be the field of q *** any positive integer n,the Wenger graph Wn(q)is defined as follows:it is a bipartite graph with the vertex partitions being two copies of the(n+1)-dimensional vector space Fq^n+1,and two vertices p=(p(1),…,p(n+1))and l=[l(1),…,l(n+1)]being adjacent if p(i)+l(i)=p(1)l(1)i-1,for all i=2,3,…,n+*** 2008,Shao,He and Shan showed that for n≥2,Wn(q)contains a cycle of length 2 k where 4≤k≤2 p and k≠*** this paper we extend their results by showing that(i)for n≥2 and p≥3,Wn(q)contains cycles of length 2k,where 4≤k≤4 p+1 and k≠5;(ii)for q≥5,0

关键词： cycle pancyclic finite field Wenger graph graph embeddings

Pancyclism in Claw-free Graphs

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Tsinghua Science and Technology 1998年第4期3卷 1218-1220页

作者：陆玫俞正光 Department of Applied Mathematics Tsinghua University Beijing 100084

A graph G is claw\|free if G has no induced subgraph isomorphic to K\-\{1,3\}. And a graph G is pancyclic if for every m, 3≤m≤|V(G)|, there is a cycle of length m. This paper considered neighbourhood union for any pair of nonadjacent vertices in claw\|free graph and obtained the following theorem: If G is a 2\|connected claw\|free graph of order n≥12 and |N(u)∪N(v)|+|N(u)∪N(w)|+|N(v)∪N(w)|≥2n-1 for any three pairwise nonadjacent vertices u,v, and w, then G is pancyclic.

关键词： claw\|free graph neighbourhood union pancyclic

Able群上Cayley图的哈密顿性(英文)

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新疆大学学报（自然科学版） 2003年第1期20卷 14-21页

作者：马合木提.阿合力别克新疆大学数学与系统科学学院新疆乌鲁木齐830046

设 G是群 ,S是 G的不含单位元的子集 ,满足 S=S1 ,G的相对于 S的 Cayley图 ,是一个以 G为顶点集的无向图 ,对 G的任意两上元 x和 y,x和 y在 C( G,S)中相邻 ,当且今当 x1 y∈ S.本文中我们得到了以下结论 :( i)设 G是阶至少为 2的有限 A... 详细信息

设 G是群 ,S是 G的不含单位元的子集 ,满足 S=S1 ,G的相对于 S的 Cayley图 ,是一个以 G为顶点集的无向图 ,对 G的任意两上元 x和 y,x和 y在 C( G,S)中相邻 ,当且今当 x1 y∈ S.本文中我们得到了以下结论 :( i)设 G是阶至少为 2的有限 Abel群 .S G\{ 0 }且 S=S1 ,则 C( G,S)中每个二长路都包含在一个哈密顿圈中 .( ii)设 G是可数无限 Abel群 ,S G\{ 0 }满足 S=S1 和 | S|≥ 4 .则 C( G,S)中每个长为 2的路含在一条双向哈密顿路上 .( iii)有限 Abel群上围长为 3,阶数至少为 3的连通 Cayley图是泛圈的 .( iv)设 G是可数无限 Abel群 ,S G\{ 0 }满足 S=S1和 | S|≥ 4 .若 girth[C( G,S) ]=3,则 C( G,S)是泛圈的 .

关键词： Able群 Cayley图哈密顿性 pancyclic 无向图泛图哈密顿路