A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs

Mamadou Moustapha Kanté,Lhouari Nourine,Vincent Limouzy,Arnaud Mary,Takeaki Uno

doi:10.1007/978-3-662-53174-7_11

A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs

Mamadou Moustapha Kanté, Lhouari Nourine + Show 3 more

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https://doi.org/10.1007/978-3-662-53174-7_11

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Publication Date: Jan 1, 2016

Citations: 16

Affiliation: Institut Pascal, Laboratory of Computing, Modelling and Optimization of the Systems, Clermont Université, French National Centre for Scientific Research, Claude Bernard University Lyon 1, Biometry and Evolutionary Biology Laboratory, National Institute of Informatics

#Sets In Graphs #Chordal Graphs + Show 5 more

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Abstract

An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial algorithm for listing the set of minimal hitting sets in hypergraphs. We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an important and well-studied graph class where such an algorithm was open for a while.

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