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    A dichotomy for upper domination in monogenic classes

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    Type
    Article
    Authors
    AbouEisha, Hassan M. cc
    Hussain, Shahid cc
    Lozin, Vadim V.
    Monnot, Jérôme
    Ries, Bernard
    KAUST Department
    Computer Science Program
    Date
    2014-11-14
    Online Publication Date
    2014-11-13
    Print Publication Date
    2014
    Embargo End Date
    2015-11-14
    Permanent link to this record
    http://hdl.handle.net/10754/563271
    
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    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.
    Publisher
    Springer International Publishing
    Journal
    Combinatorial Optimization and Applications
    DOI
    10.1007/978-3-319-12691-3_20
    Additional Links
    https://basepub.dauphine.fr//bitstream/123456789/16160/2/COCOA14_UDS.pdf
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-12691-3_20
    Scopus Count
    Collections
    Articles; Computer Science Program

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