Lifting facets of the cut polytope

Authors:
Caterina De Simone
Affiliations:
IAC, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 Roma, Italy and RUTCOR, Rutgers University, New Brunswick, NJ 08903, USA
Venue:
Operations Research Letters
Year:
1990

Citing 5
Cited 1

Theory of linear and integer programming

Theory of linear and integer programming
On the cut polytope

Mathematical Programming: Series A and B
Integer and combinatorial optimization

Integer and combinatorial optimization
Graphs and Hypergraphs

Graphs and Hypergraphs
Graph Theory With Applications

Graph Theory With Applications

A simultaneous lifting strategy for identifying new classes of facets for the Boolean quadric polytope

Operations Research Letters

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Abstract

The cut polytope P"c(G) of a graph G is the convex hull of the incidence vectors of the edge sets of all cuts of G. We give a sufficient condition for an inequality defining a facet of P"c(G) to define a facet of the cut polytope of a graph containing G as an induced subgraph. Our result generalizes a result of Deza stating that if G is a complete graph with more than two vertices, then an inequality defines a facet of P"c(G) if and only if it defines a facet of the cut polytope of every complete graph containing G.