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Edge-Fault-Tolerant Edge-Bipancyclicity of Bubble-Sort Graphs 被引量:1
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作者 Xin Ping XU Min XU Jin JING 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第4期675-686,共12页
The bubble-sort graph Bn is a bipartite graph. Kikuchi and Araki [Edge-bipancyclicity and edge-fault-tolerant bipancyclicity of bubble-sort graphs. Information Processing Letters, 100, 52- 59 (2006)] have proved tha... The bubble-sort graph Bn is a bipartite graph. Kikuchi and Araki [Edge-bipancyclicity and edge-fault-tolerant bipancyclicity of bubble-sort graphs. Information Processing Letters, 100, 52- 59 (2006)] have proved that Bn is edge-bipancyclic for n ≤ 5 and Bn - F is bipancyclic when n ≥ 4 and IFI≤ n - 3. In this paper, we improve this result by showing that for any edge set F of Bn with IFI ≤ n - 3, every edge of Bn - F lies on a cycle of every even length from 6 to n! for n≤ 5 and every edge of Bn - F lies on a cycle of every even length from 8 to n! for n = 4. 展开更多
关键词 Cycles bipancyclicity fault tolerance bubble-sort graph
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A LOCALIZATION CONDITION FORBIPANCYCLIC BIPARTITE GRAPHS
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作者 SHI Ronghua (Department of Applied Mathematics, Naming University of Science and Technology,Nanjing 210094, China)LOU Dingjun (Department of Computer Science, Zhongshan University, Guangzhou 510275, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1997年第1期61-65,共5页
In this paper we prove the following: Let G be connected balanced bipartite graph of order 2n> 4. If G satisfies the localization condition |NZ(u)\N(v)| + 2 < d(u), for any u,v∈ V(G) and d(u, v) = 3 where N(u) ... In this paper we prove the following: Let G be connected balanced bipartite graph of order 2n> 4. If G satisfies the localization condition |NZ(u)\N(v)| + 2 < d(u), for any u,v∈ V(G) and d(u, v) = 3 where N(u) = {w|w∈V(G) and d(u, w)= 2}, then G is either bipancyclic or isomorphic to C6. Furthermore, a conjecture is proposed. 展开更多
关键词 Localization CONDITION CONNECTED BALANCED BIPARTITE GRAPH bipancyclic ISOMORPHIC
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EDGE CONDITION FOR A HAMILTONIAN BIPARTITE GRAPH TO BE BIPANCYCLIC
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作者 HU Zhiquan(Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079 Institute ofSystems Science, Academy of Mathematics and Systems Sciences,Chinese Academy of Sciences, Beijing 100080, China) 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2003年第4期527-532,共6页
Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeic... Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel. 展开更多
关键词 bipartite graph bipancyclic HAMILTONIAN
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BIPANCYCLISM IN HAMILTONIAN BIPARTITE GRAPHS
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作者 田丰 臧文安 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1989年第1期22-31,共10页
It is shown that if G is a hamiltonian bipartite graph on 2n vertices and δ(G)】2n/5+2,where n≥60,then G is bipancyclic.
关键词 HAMILTONIAN BIPARTITE GRAPHS bipancyclism
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Binding Number, Minimum Degree and Bipancyclism in Bipartite Graphs
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作者 SUN Jing HU Zhiquan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2016年第5期448-452,共5页
Let G =(V1,V2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =Kn and min i∈{1,2}|N(S)|〈n min |N(S)|/|S|otherwise.We call G b... Let G =(V1,V2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =Kn and min i∈{1,2}|N(S)|〈n min |N(S)|/|S|otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B(G) 〉 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows:Let 0 〈 c 〈 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n(n is large enough) vertices such that B(G) c and δ(G)(2-c)n/(3-c)+2/3.Then G is bipancyclic. 展开更多
关键词 balanced bipartite graph HAMILTONIAN bipancyclism bipartite binding number minimum degree
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