Single-source three-disjoint path covers in cubes of connected graphs

Park, Jung-Heum; Ihm, Insung

doi:10.1016/j.ipl.2013.04.012

Cited by 16 publications

(2 citation statements)

References 24 publications

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“…The structure of the cubes of connected graphs was investigated with respect to single-source 3-disjoint path covers [24]. The problem was also investigated in view of a full utilization of nodes in interconnection networks [25].…”

Section: Disjoint Path Coversmentioning

confidence: 99%

Disjoint path covers in cubes of connected graphs

Park

Ihm

2014

Discrete Mathematics

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Given a graph G, and two vertex sets S and T of size k each, a many-tomany k-disjoint path cover of G joining S and T is a collection of k disjoint paths between S and T that cover every vertex of G. It is classified as paired if each vertex of S must be joined to a designated vertex of T , or unpaired if there is no such constraint. In this article, we first present a necessary and sufficient condition for the cube of a connected graph to have a paired 2-disjoint path cover. Then, a corresponding condition for the unpaired type of 2-disjoint path cover problem is immediately derived. It is also shown that these results can easily be extended to determine if the cube of a connected graph has a hamiltonian path from a given vertex to another vertex that passes through a prescribed edge.

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Section: Disjoint Path Coversmentioning

confidence: 99%

Disjoint path covers in cubes of connected graphs

Park

Ihm

2014

Discrete Mathematics

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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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One-to-One Disjoint Path Covers on Mesh

Fan

Han

et al. 2015

Algorithms and Architectures for Parallel Processing

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Single-source three-disjoint path covers in cubes of connected graphs

Cited by 16 publications

References 24 publications

Disjoint path covers in cubes of connected graphs

Disjoint path covers in cubes of connected graphs

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

One-to-One Disjoint Path Covers on Mesh

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