Connected Domination

Chellali, Mustapha; Favaron, Odile

doi:10.1007/978-3-030-51117-3_4

Cited by 3 publications

(3 citation statements)

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“…The CDS and MLST problems are shown to be NP-hard for several classes: bipartite graphs [32], cubic graphs [28] and unit disk graphs [6]. On the other hand, polynomial-time algorithms were designed for other classes: cographs [7], distance-hereditary graphs [11] and cocomparability graphs [27] (see the detail in [5]).…”

Section: Related Resultsmentioning

confidence: 99%

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Connected domination in grid graphs

Goto¹,

Kobayashi²

2021

Preprint

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Given an undirected simple graph, a subset of the vertices of the graph is a dominating set if every vertex not in the subset is adjacent to at least one vertex in the subset. A subset of the vertices of the graph is a connected dominating set if the subset is a dominating set and the subgraph induced by the subset is connected. In this paper, we determine the minimum cardinality of a connected dominating set, called the connected domination number, of an m × n grid graph for any m and n.

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Section: Related Resultsmentioning

confidence: 99%

“…(8) 7)). D contains either (1,4) or (1,5) to dominate (1,4), and (1, 5) ∈ D holds because D is connected. Then, since D is (0, 5)-(1, 5)-regular, D ′ which is (0, 5)-(m, 5)-regular can be constructed from D by applying Lemma 4.12 m − 1 times (Fig.…”

Section: Routine Feasibilitymentioning

confidence: 99%