KAUST DepartmentComputer Science Program
Online Publication Date2014-11-13
Print Publication Date2014
Embargo End Date2015-11-14
Permanent link to this recordhttp://hdl.handle.net/10754/563271
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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.
CitationAbouEisha, H., Hussain, S., Lozin, V., Monnot, J., & Ries, B. (2014). A Dichotomy for Upper Domination in Monogenic Classes. Lecture Notes in Computer Science, 258–267. doi:10.1007/978-3-319-12691-3_20