Irreversible 2-conversion set in graphs of bounded degree Kyncl, Jan Lidicky, Bernard Lidicky, Bernard Vyskocil, Tomas
dc.contributor.department Mathematics 2018-10-29T21:14:07.000 2020-06-30T06:00:14Z 2020-06-30T06:00:14Z Sun Jan 01 00:00:00 UTC 2017 2017-09-26
dc.description.abstract <p>An irreversible k-threshold process (also a k-neighbor bootstrap percolation) is a dynamic process on a graph where vertices change color from white to black if they have at least k black neighbors. An irreversible k-conversion set of a graph G is a subset S of vertices of G such that the irreversible k-threshold process starting with the vertices of S black eventually changes all vertices of G to black. We show that deciding the existence of an irreversible 2-conversion set of a given size is NP-complete, even for graphs of maximum degree 4, which answers a question of Dreyer and Roberts. Conversely, we show that for graphs of maximum degree 3, the minimum size of an irreversible 2-conversion set can be computed in polynomial time. Moreover, we find an optimal irreversible 3-conversion set for the toroidal grid, simplifying constructions of Pike and Zou.</p>
dc.description.comments <p>This article is published as Vyskočil, Tomáš, Bernard Lidický, and Jan Kynčl. "Irreversible 2-conversion set in graphs of bounded degree." <em>Discrete Mathematics & Theoretical Computer Science</em> 19 (2017): 5. doi: <a href="" target="_blank">10.23638/DMTCS-19-3-5</a>.</p>
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dc.identifier archive/
dc.identifier.articleid 1195
dc.identifier.contextkey 13194045
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/187
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 21:45:53 UTC 2022
dc.source.uri 10.23638/DMTCS-19-3-5
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.disciplines Mathematics
dc.subject.keywords irreversible k-conversion process
dc.subject.keywords spread of infection
dc.subject.keywords bootstrap percolation
dc.subject.keywords NP-complete problem
dc.subject.keywords matroid parity problem
dc.subject.keywords toroidal grid
dc.title Irreversible 2-conversion set in graphs of bounded degree
dc.type article
dc.type.genre article
dspace.entity.type Publication
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relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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