On the number of maximal bipartite subgraphs of a graph

Authors:
Jesper Makholm Byskov;Bolette Ammitzbøll Madsen;Bjarke Skjernaa
Affiliations:
Department of Computer Science, University of Aarhus, Denmark;Department of Computer Science, University of Aarhus, Denmark;Department of Computer Science, University of Aarhus, Denmark
Venue:
Journal of Graph Theory
Year:
2005

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Abstract

We show new lower and upper bounds on the maximum number ofmaximal induced bipartite subgraphs of graphs with nvertices. We present an infinite family of graphs having105n-10 ≈ 1.5926n; suchsubgraphs show an upper bound of O(12n-4)= O(1.8613n) and give an algorithm thatfinds all maximal induced bipartite subgraphs in time within apolynomial factor of this bound. This algorithm is used in theconstruction of algorithms for checking k-colorability of agraph. © 2004 Wiley Periodicals, Inc. J Graph Theory 48:127132, 2005