Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6658
Title: Globally minimal defensive alliances
Authors: GAIKWAD, AJINKYA
MAITY, SOUMEN
Dept. of Mathematics
Keywords: Algorithms
FPT
Treewidth
W[1]-hard
2022-MAR-WEEK2
TOC-MAR-2022
2022
Issue Date: Aug-2022
Publisher: Elsevier B.V.
Citation: Information Processing Letters, 177, 106253.
Abstract: A defensive alliance in an undirected graph is a nonempty set of vertices S satisfying the condition that every vertex has at least as many neighbours (including itself) in S as it has in . We consider the notion of global minimality in this paper. We are interested in globally minimal defensive alliance of maximum size. This problem is known to be NP-hard but its parameterized complexity remains open until now. We enhance our understanding of the problem from the viewpoint of parameterized complexity by showing that the Globally Minimal Defensive Alliance problem is W[1]-hard when parameterized by the treewidth of the graph. We also present a polynomial-time algorithm when the input graph happens to be a tree.
URI: https://doi.org/10.1016/j.ipl.2022.106253
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6658
ISSN: 0020-0190
Appears in Collections:JOURNAL ARTICLES

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