Fault-tolerant hamiltonian laceability of hypercubes

Tsai, Chang-Hsiung; Tan, Jinglu; Liang, Tyne; Hsu, Lih‐Hsing

doi:10.1016/s0020-0190(02)00214-4

Cited by 98 publications

(29 citation statements)

References 3 publications

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“…Theorem 2.4 shows that Q n is (n−2)-edge-faulttolerant hamiltonian laceable and strongly hamiltonian laceable for n 2. This result was also obtained by Tsai et al [141], independently. Hsieh and Kuo [74], and Tsai et al [141] showed that Q n is (n − 3)-edge-fault-tolerant hyper hamiltonian laceable for n 3.…”

Section: Theorem 22 (Tsai and Jiangsupporting

confidence: 84%

“…This result was also obtained by Tsai et al [141], independently. Hsieh and Kuo [74], and Tsai et al [141] showed that Q n is (n − 3)-edge-fault-tolerant hyper hamiltonian laceable for n 3. Sun et al 1) proved that Q n is (n − 3)-fault-tolerant hamiltonian laceable and strongly hamiltonian laceable and hyper hamiltonian laceable for n 3 if f av + f e n − 3.…”

Section: Theorem 22 (Tsai and Jiangsupporting

confidence: 84%

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Survey on path and cycle embedding in some networks

2009

Front. Math. China

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To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic problem. A stronger concept than the pancylicity is the panconnectivity. A graph of order n is said to be panconnected if for any pair of different vertices x and y with distance d there exist xy-paths of every length from d to n. The pancyclicity or the panconnectivity is an important property to determine if the topology of a network is suitable for some applications where mapping cycles or paths of any length into the topology of the network is required. The pancyclicity and the panconnectivity of interconnection networks have attracted much research interest in recent years. A large amount of related work appeared in the literature, with some repetitions. The purpose of this paper is to give a survey of the results related to these topics for the hypercube and some hypercube-like networks.

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Section: Theorem 22 (Tsai and Jiangsupporting

confidence: 84%

Section: Theorem 22 (Tsai and Jiangsupporting

confidence: 84%

Survey on path and cycle embedding in some networks

2009

Front. Math. China

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“…First, every hypercube has a perfect matching, and second, every hypercube is Hamiltonian laceable, that is, there is a Hamiltonian path in it between any two vertices from different partite sets. Both facts are well-known and easy to prove (in fact, the same is true even after deleting up to n − 2 edges in Q n , see [22]). Note that the second fact implies that if we delete one vertex from each partite set of a hypercube, the resulting graph still has a Hamiltonian path, and hence a perfect matching.…”

Section: Proposition 41 (Yang and Linmentioning

confidence: 72%

Generalized Matching Preclusion in Bipartite Graphs

Wheeler¹,

Cheng

Ferranti³

et al. 2018

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The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex, whose deletion creates an isolated vertex, which is an obstruction to the existence of a perfect matching. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes.

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“…Readers can refer [4] for a survey on the properties of hypercubes. The following theorem is proven by Tsai et al [6].…”

Section: Preliminariesmentioning

confidence: 83%