, Volume 6, Issue 1, pp 48-61

Properties of vertex packing and independence system polyhedra

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Abstract

We consider two convex polyhedra related to the vertex packing problem for a finite, undirected, loopless graphG with no multiple edges. A characterization is given for the extreme points of the polyhedron \(\mathcal{L}_G = \{ x \in R^n :Ax \leqslant 1_m ,x \geqslant 0\} \) , whereA is them × n edge-vertex incidence matrix ofG and 1 m is anm-vector of ones. A general class of facets of = convex hull{xR n :Ax≤1 m ,x binary} is described which subsumes a class examined by Padberg [13]. Some of the results for are extended to a more general class of integer polyhedra obtained from independence systems.

This research was supported by the National Science Foundation under Grant GK-32282X to Cornell University and by the United States Army under Contract No. DA-31-124-ARO-D-462 to the Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, U.S.A.