# On the facial structure of set packing polyhedra

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## Abstract

In this paper we address ourselves to identifying facets of the set packing polyhedron, i.e., of the convex hull of integer solutions to the set covering problem with equality constraints and/or constraints of the form “⩽”. This is done by using the equivalent node-packing problem derived from the intersection graph associated with the problem under consideration. First, we show that the cliques of the intersection graph provide a first set of facets for the polyhedron in question. Second, it is shown that the cycles without chords of odd length of the intersection graph give rise to a further set of facets. A rather strong geometric property of this set of facets is exhibited.

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## Copyright information

© The Mathematical Programming Society 1973