Edge-fault-tolerant hamiltonicity of locally twisted cubes under conditional edge faults

Hsieh, Sun Yuan; Wu, Chang‐Yu

doi:10.1007/s10878-008-9157-x

Cited by 59 publications

(17 citation statements)

References 23 publications

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“…Yang et al [33] proved that LTQ n is n-connected and has diameter nþ3 2 AE Ç (respectively, n À 1) for n P 5 (respectively, n = 3, 4). The locally twisted cube has already drawn many researchers' attention [10][11][12]14,21,22,[31][32][33].…”

Section: Definition 1 [33]mentioning

confidence: 99%

Flexible cycle embedding in the locally twisted cube with nodes positioned at any prescribed distance

Kung¹

2013

Information Sciences

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Section: Definition 1 [33]mentioning

confidence: 99%

Flexible cycle embedding in the locally twisted cube with nodes positioned at any prescribed distance

Kung¹

2013

Information Sciences

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“…One advantage of LTQ n is that the diameter is only about half of the diameter of an n-dimensional hypercube. For more properties of LTQ n , the reader can refer to [2,12,13,19,25,32].…”

Section: Constructing Spanning Trees In Locally Twisted Cubesmentioning

confidence: 99%

Independent spanning trees vs. edge-disjoint spanning trees in locally twisted cubes

Lin

Yang

Hsu

et al. 2010

Information Processing Letters

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“…In addition, the Hamiltonian cycle problem on hexagonal grid graphs was known to be NP-complete [18]. For more related works, we refer readers to [5,7,9,13,15,16,17,24,27,28,29,36].…”

Section: Introductionmentioning

confidence: 99%

The Hamiltonian properties of supergrid graphs

Hung

Yao

Chan

2015

Theoretical Computer Science

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In this paper, we first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be NP-complete. However, they are unknown for supergrid graphs. The Hamiltonian cycle (path) problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines. In this paper, we will prove that the Hamiltonian cycle problem for supergrid graphs is NP-complete. It is easily derived from the Hamiltonian cycle result that the Hamiltonian path problem on supergrid graphs is also NP-complete. We then show that two subclasses of supergrid graphs, including rectangular (parallelism) and alphabet, always contain Hamiltonian cycles.

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Edge-fault-tolerant hamiltonicity of locally twisted cubes under conditional edge faults

Cited by 59 publications

References 23 publications

Flexible cycle embedding in the locally twisted cube with nodes positioned at any prescribed distance

Flexible cycle embedding in the locally twisted cube with nodes positioned at any prescribed distance

Independent spanning trees vs. edge-disjoint spanning trees in locally twisted cubes

The Hamiltonian properties of supergrid graphs

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