Enumerating Minimal Connected Dominating Sets in Graphs of Bounded Chordality
Listing, generating or enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality. We establish enumeration algorithms as well as lower and upper bounds for the maximum number of minimal connected dominating sets in such graphs. In particular, we present algorithms to enumerate all minimal connected dominating sets of chordal graphs in time O(1.7159^n), of split graphs in time O(1.3803^n), and of AT-free, strongly chordal, and distance-hereditary graphs in time O^*(3^{n/3}), where n is the number of vertices of the input graph. Our algorithms imply corresponding upper bounds for the number of minimal connected dominating sets for these graph classes.
Minimal connected dominating set
exact algorithms
enumeration
307-318
Regular Paper
Petr A.
Golovach
Petr A. Golovach
Pinar
Heggernes
Pinar Heggernes
Dieter
Kratsch
Dieter Kratsch
10.4230/LIPIcs.IPEC.2015.307
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