# Properties of vertex packing and independence system polyhedra

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DOI: 10.1007/BF01580222

- Cite this article as:
- Nemhauser, G.L. & Trotter, L.E. Mathematical Programming (1974) 6: 48. doi:10.1007/BF01580222

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## Abstract

We consider two convex polyhedra related to the vertex packing problem for a finite, undirected, loopless graph

*G*with no multiple edges. A characterization is given for the extreme points of the polyhedron\(\mathcal{L}_G = \{ x \in R^n :Ax \leqslant 1_m ,x \geqslant 0\} \), where*A*is the*m × n*edge-vertex incidence matrix of*G*and 1_{m}is an*m*-vector of ones. A general class of facets of = convex hull{*x*∈**R**^{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.## Copyright information

© The Mathematical Programming Society 1974