Complexity of paired domination in AT-free and planar graphs

Tripathi, Vikash; Kloks, Ton; Pandey, Arti; Paul, Kaustav; Wang, Hung-Lung

doi:10.1016/j.tcs.2022.07.010

Cited by 4 publications

(1 citation statement)

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“…It is well-known that given a graph G and an integer k, the problem of deciding if there is a PD-set in G of cardinality at most k is NP-complete [17], even for bipartite graphs [24], split graphs [24] or planar graphs [36]. Thus, most of the papers, as for example [1,5,8,22,24,25,28,32,36] and the references therein, focus on studying the complexity of computing the paired domination number in several restricted graph classes.…”

Section: Introductionmentioning

confidence: 99%

Paired and semipaired domination in triangulations

Claverol¹,

Hernando²,

Maureso³

et al. 2022

Preprint

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A dominating set of a graph G is a subset D of vertices such that every vertex not in D is adjacent to at least one vertex in D. A dominating set D is paired if the subgraph induced by its vertices has a perfect matching, and semipaired if every vertex in D is paired with exactly one other vertex in D that is within distance 2 from it. The paired domination number, denoted by γ pr (G), is the minimum cardinality of a paired dominating set of G, and the semipaired domination number, denoted by γ pr2 (G), is the minimum cardinality of a semipaired dominating set of G. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that γ pr (G) ≤ 2 n 4 for any neartriangulation G of order n ≥ 4, and that with some exceptions, γ pr2 (G) ≤ 2n 5 for any near-triangulation G of order n ≥ 5.

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