Mathematical Programming

, Volume 56, Issue 1, pp 121–160

Facets for the cut cone I

  • Michel Deza
  • Monique Laurent

DOI: 10.1007/BF01580897

Cite this article as:
Deza, M. & Laurent, M. Mathematical Programming (1992) 56: 121. doi:10.1007/BF01580897


We study facets of the cut coneCn, i.e., the cone of dimension 1/2n(n − 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a “lifting” procedure for constructing facets ofCn+1 from given facets of the lower dimensional coneCn. After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.

Key words

Max-cut problem cone polytope facet lifting hypermetric inequality 

Copyright information

© The Mathematical Programming Society, Inc. 1992

Authors and Affiliations

  • Michel Deza
    • 1
  • Monique Laurent
    • 2
  1. 1.CNRS, Université Paris VIIParis 05France
  2. 2.CNRS, LAMSADE, Université Paris DauphineParis 16France