Mathematical Programming

, Volume 6, Issue 1, pp 48–61

Properties of vertex packing and independence system polyhedra

  • G. L. Nemhauser
  • L. E. TrotterJr.

DOI: 10.1007/BF01580222

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


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 1m is anm-vector of ones. A general class of facets of
= convex hull{xRn:Ax≤1m,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

Authors and Affiliations

  • G. L. Nemhauser
    • 1
  • L. E. TrotterJr.
    • 1
  1. 1.Cornell UniversityIthacaUSA
  2. 2.Department of Administrative SciencesYale UniversityNew HavenUSA