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. © 2011 Springer-Verlag.
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CITATION STYLE
Kanté, M. M., Limouzy, V., Mary, A., & Nourine, L. (2011). Enumeration of minimal dominating sets and variants. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6914 LNCS, pp. 298–309). https://doi.org/10.1007/978-3-642-22953-4_26
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