Enumeration of minimal dominating sets and variants

Authors:
Mamadou Moustapha Kanté;Vincent Limouzy;Arnaud Mary;Lhouari Nourine
Affiliations:
Clermont-Université, Université Blaise Pascal, LIMOS, CNRS, France;Clermont-Université, Université Blaise Pascal, LIMOS, CNRS, France;Clermont-Université, Université Blaise Pascal, LIMOS, CNRS, France;Clermont-Université, Université Blaise Pascal, LIMOS, CNRS, France
Venue:
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Year:
2011

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Abstract

In this paper, we are interested in the enumeration of minimal dominating sets in graphs. A polynomial delay algorithm with polynomial space in split graphs is presented. We then introduce a notion of maximal extension (a set of edges added to the graph) that keeps invariant the set of minimal dominating sets, and show that graphs with extensions as split graphs are exactly the ones having chordal graphs as extensions. We finish by relating the enumeration of some variants of dominating sets to the enumeration of minimal transversals in hypergraphs.