Enumerating maximal independent sets with applications to graph colouring

Authors:
Jesper Makholm Byskov
Affiliations:
BRICS22Basic Research in Computer Science (www.brics.dk), funded by the Danish National Research Foundation., Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, DK-8200 ...
Venue:
Operations Research Letters
Year:
2004

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Abstract

We give tight upper bounds on the number of maximal independent sets of size k (and at least k and at most k) in graphs with n vertices. As an application of the proof, we construct improved algorithms for graph colouring and computing the chromatic number of a graph.