Many-to-many n-disjoint path covers in n-dimensional hypercubes

Liu, Di; Li, Jing

doi:10.1016/j.ipl.2010.05.004

Cited by 16 publications

(2 citation statements)

References 14 publications

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“…Given S and T in a graph G, it is NP-complete to determine if there exists a one-to-one, one-to-many, or many-to-many k-DPC joining S and T for any fixed k ≥ 1 [32,33]. The disjoint path cover problems have been studied for graphs such as hypercubes [5,6,7,10,13,19,24], recursive circulants [20,21,32,33], and hypercube-like graphs [18,22,28,33], cube of a connected graph [29,30], and k-ary n-cubes [35,37]. Necessary conditions for a graph G to be f -fault many-to-many k-disjoint path coverable have been established in terms of its connectivity κ(G) and its minimum degree δ(G) [32,33], as shown below.…”

Section: Introductionmentioning

confidence: 99%

Many-to-many two-disjoint path covers in restricted hypercube-like graphs

Kim

Park

2014

Theoretical Computer Science

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A Disjoint Path Cover (DPC for short) of a graph is a set of pairwise (internally) disjoint paths that altogether cover every vertex of the graph. Given a set S of k sources and a set T of k sinks, a many-to-many k-DPC between S and T is a disjoint path cover each of whose paths joins a pair of source and sink. It is classified as paired if each source of S must be joined to a designated sink of T , or unpaired if there is no such constraint. In this paper, we show that every m-dimensional restricted hypercube-like graph with at most m − 3 faulty vertices and/or edges being removed has a paired (and unpaired) 2-DPC joining arbitrary two sources and two sinks where m ≥ 5. The bound m − 3 on the number of faults is optimal for both paired and unpaired types.

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Section: Introductionmentioning

confidence: 99%

Many-to-many two-disjoint path covers in restricted hypercube-like graphs

Kim

Park

2014

Theoretical Computer Science

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“…The paired 2-DPC consisting of two paths of equal length was suggested in [8]. The disjoint path cover problem has also been studied for some bipartite graphs: paired DPC's for hypercubes [7] and for hypercubes with faulty vertices [6]; unpaired DPC's for hypercubes [3,9] and for bipartite graphs obtained by adding some edges to hypercubes [4].…”

Section: Introductionmentioning

confidence: 99%

General-demand disjoint path covers in a graph with faulty elements

Lee

Park

2012

International Journal of Computer Mathematics

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A k-disjoint path cover of a graph is a set of k internally vertex-disjoint paths which cover the vertex set with k paths and each of which runs between a source and a sink. Given that each source and sink v is associated with an integer-valued demand d(v) ≥ 1, we are concerned with general-demand k-disjoint path cover in which every source and sink v is contained in the d(v) paths. In this paper, we present a reduction of a general-demand disjoint path cover problem to an unpaired many-to-many disjoint path cover problem, and obtain some results on disjoint path covers of restricted HL-graphs and proper interval graphs with faulty vertices and/or edges.

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One-to-one disjoint path covers in hypercubes with faulty edges

Wang

Zhao

2019

J Supercomput

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Many-to-many n-disjoint path covers in n-dimensional hypercubes

Cited by 16 publications

References 14 publications

Many-to-many two-disjoint path covers in restricted hypercube-like graphs

Many-to-many two-disjoint path covers in restricted hypercube-like graphs

General-demand disjoint path covers in a graph with faulty elements

One-to-one disjoint path covers in hypercubes with faulty edges

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