A Dichotomy for Upper Domination in Monogenic Classes

Hassan Aboueisha (1) , Shahid Hussain (1) , Vadim Lozin (2) , Jérôme Monnot (3) , Bernard Ries (3)

1 Center for Numerical Porous Media (NumPor) - King Abdullah University of Science and Technology
2 DIMAP - Centre for Discrete Mathematics and its Applications [Warwick]
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

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.

Mots clés: graphs

Domaines: Informatique [cs]

Hassan Aboueisha, Shahid Hussain, Vadim Lozin, Jérôme Monnot, Bernard Ries. A Dichotomy for Upper Domination in Monogenic Classes. 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2014), Dec 2014, Wailea, Maui, HI, United States. pp.258-267, ⟨10.1007/978-3-319-12691-3_20⟩. ⟨hal-01434163⟩