Stable skew partition problem

Authors:
Simone Dantas;Celina M. H. de Figueiredo;Sulamita Klein;Sylvain Gravier;Bruce A. Reed
Affiliations:
COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;IM and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro 21945-970, RJ, Brazil;IM and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro 21945-970, RJ, Brazil;CNRS, GeoD research group, "Maths à modeler" project, Laboratoire Leibniz, Grenoble, France;Scholl of Computer Science, McGill University, McGill University, 3480 University Street, Montreal, Quebeck, Canada H3A 2A7 Canada
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

A skew partition is a partition of the vertex set of a graph into four nonempty parts A,B, C,D such that there are all possible edges between A and B, and no edges between C and D. A stable skew partition is a skew partition where A induces a stable set of the graph. We show that determining if a graph permits a stable skew partition is NP-complete. We discuss limits of such reductions by adding cardinality constraints.