Paired many-to-many disjoint path covers of hypertori

Kronenthal, Brian G.; Wong, Tony W. H.

doi:10.1016/j.dam.2016.09.020

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2018

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Cited by 6 publications

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“…In addition, the problem is concerned with applications where full utilization of network nodes is important [3]. The problems have been studied for various classes of graphs, such as interval graphs [4,5], hypercubes [6,7,8], torus networks [9,10,11,12], dense graphs [13], and cubes of connected graphs [14,15].…”

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confidence: 99%

Paired Many-to-Many 3-Disjoint Path Covers in Bipartite Toroidal Grids

Park¹

2018

JCSE

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Given two disjoint vertex-sets, S = {s1,. .. , s k } and T = {t1,. .. , t k } in a graph, a paired many-to-many k-disjoint path cover joining S and T is a set of pairwise vertex-disjoint paths {P1,. .. , P k } that altogether cover every vertex of the graph, in which each path Pi runs from si to ti. In this paper, we first study the disjoint-path-cover properties of a bipartite cylindrical grid. Based on the findings, we prove that every bipartite toroidal grid, excluding the smallest one, has a paired many-to-many 3-disjoint path cover joining S = {s1, s2, s3} and T = {t1, t2, t3} if and only if the set S ∪ T contains the equal numbers of vertices from different parts of the bipartition.

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