A dichotomy for upper domination in monogenic classes

Embargo End Date
2015-11-14

Type
Article

Authors
AbouEisha, Hassan M.
Hussain, Shahid
Lozin, Vadim V.
Monnot, Jérôme
Ries, Bernard

KAUST Department
Computer Science Program

Online Publication Date
2014-11-13

Print Publication Date
2014

Date
2014-11-14

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.

Citation
AbouEisha, 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

Publisher
Springer Nature

Journal
Lecture Notes in Computer Science

DOI
10.1007/978-3-319-12691-3_20

Additional Links
https://basepub.dauphine.fr//bitstream/123456789/16160/2/COCOA14_UDS.pdf

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