Exponential time algorithms for the minimum dominating set problem on some graph classes

Authors:
Serge Gaspers;Dieter Kratsch;Mathieu Liedloff
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;LITA, Université de Paul Verlaine – Metz, Metz, France;LITA, Université de Paul Verlaine – Metz, Metz, France
Venue:
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Year:
2006

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Abstract

The Minimum Dominating Set problem remains NP-hard when restricted to chordal graphs, circle graphs and c-dense graphs (i.e. |E| ≥cn2 for a constant c, 0cO(1.4173n) for chordal graphs, O(1.4956n) for circle graphs, and $O(1.2303^{(1+\sqrt{1-2c})n})$ for c-dense graphs