Hamiltonian-laceability of star graphs

Hsieh, Sun Yuan; Chen, Gen Huey; Ho, Chin Wen

doi:10.1002/1097-0037(200012)36:4<225::aid-net3>3.0.co;2-g

Cited by 100 publications

(32 citation statements)

References 22 publications

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“…The Hamiltonian-laceability of the hierarchical hypercube network is still open. More specifically, is the hierarchical hypercube network Hamiltonian-laceable or strongly Hamiltonian-laceable (see [5,7])? Besides, fault-tolerant embedding on the hierarchical hypercube network was not studied before.…”

Section: Discussionmentioning

confidence: 99%

Finding cycles in hierarchical hypercube networks

Chen

et al. 2008

Information Processing Letters

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Section: Discussionmentioning

confidence: 99%

Finding cycles in hierarchical hypercube networks

Chen

et al. 2008

Information Processing Letters

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“…As in [6], a bipartite graph G is said to be strongly Hamiltonian-laceable if every two vertices x, y are joined by a Hamilton path if they are from distinct color classes, and by a path of length |V (G)| − 2 if they are from the same color class. The following result was proved in [6]:…”

Section: Definitionmentioning

confidence: 99%

Disjoint Hamilton cycles in the star graph

Čada¹,

Kaiser²,

Rosenfeld³

et al. 2009

Information Processing Letters

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“…We call v 0 and v k the end-vertices of the path. In addition, a path may contain a subpath, denoted as [7] if there is a simple path of length |V 0 | + |V 1 | − 2 between any two nodes of the same partite set. A Hamiltonian-laceable graph G = (V 0 ∪ V 1 , E) is hyper-Hamiltonian laceable [10] if for any vertex v ∈ V i , i = 0, 1, there is a Hamiltonian path of G − v between any two vertices of V 1−i .…”

Section: Preliminariesmentioning

confidence: 99%

Edge-bipancyclicity of a hypercube with faulty vertices and edges

Hsieh

Shen

2008

Discrete Applied Mathematics

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A bipartite graph G = (V , E) is said to be bipancyclic if it contains a cycle of every even length from 4 to |V |. Furthermore, a bipancyclic G is said to be edge-bipancyclic if every edge of G lies on a cycle of every even length. Let F v (respectively, F e ) be the set of faulty vertices (respectively, faulty edges) in an n-dimensional hypercube Q n . In this paper, we show that every edge of Q n − F v − F e lies on a cycle of every even length from 4 to 2 n − 2|F v | even if |F v | + |F e | n − 2, where n 3. Since Q n is bipartite of equal-size partite sets and is regular of vertex-degree n, both the number of faults tolerated and the length of a longest fault-free cycle obtained are worst-case optimal.

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Hamiltonian-laceability of star graphs

Cited by 100 publications

References 22 publications

Finding cycles in hierarchical hypercube networks

Finding cycles in hierarchical hypercube networks

Disjoint Hamilton cycles in the star graph

Edge-bipancyclicity of a hypercube with faulty vertices and edges

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