A dichotomy for upper domination in monogenic classes

Handle URI:
http://hdl.handle.net/10754/563271
Title:
A dichotomy for upper domination in monogenic classes
Authors:
AbouEisha, Hassan M. ( 0000-0003-4560-7175 ) ; Hussain, Shahid ( 0000-0002-1698-2809 ) ; Lozin, Vadim V.; Monnot, Jérôme; Ries, Bernard
Abstract:
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is NP-hard for general graphs and in many restricted graph families. In the present paper, we study the computational complexity of this problem in monogenic classes of graphs (i.e. classes defined by a single forbidden induced subgraph) and show that the problem admits a dichotomy in this family. In particular, we prove that if the only forbidden induced subgraph is a P4 or a 2K2 (or any induced subgraph of these graphs), then the problem can be solved in polynomial time. Otherwise, it is NP-hard.
KAUST Department:
Computer Science Program
Publisher:
Springer Science + Business Media
Journal:
Combinatorial Optimization and Applications
Issue Date:
2014
DOI:
10.1007/978-3-319-12691-3_20
Type:
Article
ISSN:
03029743
Appears in Collections:
Articles; Computer Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorAbouEisha, Hassan M.en
dc.contributor.authorHussain, Shahiden
dc.contributor.authorLozin, Vadim V.en
dc.contributor.authorMonnot, Jérômeen
dc.contributor.authorRies, Bernarden
dc.date.accessioned2015-08-03T11:44:34Zen
dc.date.available2015-08-03T11:44:34Zen
dc.date.issued2014en
dc.identifier.issn03029743en
dc.identifier.doi10.1007/978-3-319-12691-3_20en
dc.identifier.urihttp://hdl.handle.net/10754/563271en
dc.description.abstractAn upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is NP-hard for general graphs and in many restricted graph families. In the present paper, we study the computational complexity of this problem in monogenic classes of graphs (i.e. classes defined by a single forbidden induced subgraph) and show that the problem admits a dichotomy in this family. In particular, we prove that if the only forbidden induced subgraph is a P4 or a 2K2 (or any induced subgraph of these graphs), then the problem can be solved in polynomial time. Otherwise, it is NP-hard.en
dc.publisherSpringer Science + Business Mediaen
dc.titleA dichotomy for upper domination in monogenic classesen
dc.typeArticleen
dc.contributor.departmentComputer Science Programen
dc.identifier.journalCombinatorial Optimization and Applicationsen
dc.contributor.institutionDIMAP and Mathematics Institute, University of WarwickCoventry, United Kingdomen
dc.contributor.institutionPSL, Universit´e Paris-Dauphine, Paris Cedex 16, Franceen
dc.contributor.institutionCNRS, LAMSADE UMRParis, Franceen
kaust.authorAbouEisha, Hassan M.en
kaust.authorHussain, Shahiden
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