Hyper-Hamiltonian laceability of balanced hypercubes

Lü, Huazhong; Zhang, Heping

doi:10.1007/s11227-013-1040-6

Cited by 35 publications

(13 citation statements)

References 22 publications

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“…Lü et al [13] obtained (conditional) matching preclusion number of BH n . Lü and Zhang [14] further proved that BH n is hyper-Hamiltonian laceable. Cheng et al [5] showed that there exist two vertex-disjoint path cover in BH n .…”

Section: Introductionmentioning

confidence: 95%

Fault-Tolerant Cycle Embedding in Balanced Hypercubes with Faulty Vertices and Faulty Edges

Hao

Feng

2015

J. Inter. Net.

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Let F v (resp. F e ) be the set of faulty vertices (resp. faulty edges) in the n-dimensional balanced hypercube BH n . Fault-tolerant Hamiltonian laceability in BH n with at most 2n − 2 faulty edges is obtained in [Inform. Sci. 300 (2015) 20-27]. The existence of edge-Hamiltonian cycles in BH n − F e for |F e | ≤ 2n − 2 are gotten in [Appl. Math. Comput. 244 (2014) 447-456]. Up to now, almost all results about fault-tolerance in BH n with only faulty vertices or only faulty edges. In this paper, we consider fault-tolerant cycle embedding of BH n with both faulty vertices and faulty edges, and prove that there exists a fault-free cycle of length 2 2n − 2|F v | in BH n with |F v | + |F e | ≤ 2n − 2 and |F v | ≤ n − 1 for n ≥ 2. Since BH n is a bipartite graph with two partite sets of equal size, the cycle of a length 2 2n − 2|F v | is the longest in the worst-case.

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Section: Introductionmentioning

confidence: 95%

Fault-Tolerant Cycle Embedding in Balanced Hypercubes with Faulty Vertices and Faulty Edges

Hao

Feng

2015

J. Inter. Net.

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“…Yang [23] also demonstrated that the super connectivity of BH n is 4n−4 and the super edge-connectivity of BH n is 4n − 2 for n ≥ 2. Lü et al [12] proved that BH n is hyper-Hamiltonian laceable. Cheng et al [3] proved that BH n is (n − 1)-vertex-fault-tolerant edge-bipancyclic.…”

Section: Introductionmentioning

confidence: 99%

Fault-Free Hamiltonian Cycles in Balanced Hypercubes with Conditional Edge Faults

2019

Int. J. Found. Comput. Sci.

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The balanced hypercube, BH n , is a variant of hypercube Q n . Zhou et al. [Inform. Sci. 300 (2015) 20-27] proposed an interesting problem that whether there is a fault-free Hamiltonian cycle in BH n with each vertex incident to at least two fault-free edges. In this paper, we consider this problem and show that each fault-free edge lies on a fault-free Hamiltonian cycle in BH n after no more than 4n − 5 faulty edges occur if each vertex is incident with at least two fault-free edges for all n ≥ 2. Our result is optimal with respect to the maximum number of tolerated edge faults.

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“…Yang [17] also demonstrated that the super connectivity of BH n is (4n − 4) and the super edgeconnectivity of BH n is (4n − 2) for n ≥ 2. Lü et al [12] proved that BH n is hyper-Hamiltonian laceable. Cheng et al [2] proved that BH n is (n − 1)-vertex-fault-tolerant edge-bipancyclic.…”

Section: Introductionmentioning

confidence: 99%

Edge-fault-tolerant edge-bipancyclicity of balanced hypercubes

2017

Applied Mathematics and Computation

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The balanced hypercube, BH n , is a variant of hypercube Q n . Hao et al. [Appl. Math. Comput. 244 (2014) 447-456] showed that there exists a fault-free Hamiltonian path between any two adjacent vertices in BH n with (2n − 2) faulty edges. Cheng et al. [Inform. Sci. 297 (2015) 140-153] proved that BH n is 6-edge-bipancyclic after (2n − 3) faulty edges occur for all n ≥ 2. In this paper, we improve these two results by demonstrating that BH n is 6-edge-bipancyclic even when there exist (2n − 2) faulty edges for all n ≥ 2. Our result is optimal with respect to the maximum number of tolerated edge faults.

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Hyper-Hamiltonian laceability of balanced hypercubes

Cited by 35 publications

References 22 publications

Fault-Tolerant Cycle Embedding in Balanced Hypercubes with Faulty Vertices and Faulty Edges

Fault-Tolerant Cycle Embedding in Balanced Hypercubes with Faulty Vertices and Faulty Edges

Fault-Free Hamiltonian Cycles in Balanced Hypercubes with Conditional Edge Faults

Edge-fault-tolerant edge-bipancyclicity of balanced hypercubes

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