Critical Facets of the Stable Set Polytope

Dedicated to the memory of Paul Erdős

A facet of the stable set polytope of a graph G can be viewed as a generalization of the notion of an -critical graph. We extend several results from the theory of -critical graphs to facets. The defect of a nontrivial, full-dimensional facet of the stable set polytope of a graph G is defined by . We prove the upper bound for the degree of any node u in a critical facet-graph, and show that can occur only when . We also give a simple proof of the characterization of critical facet-graphs with defect 2 proved by Sewell [11]. As an application of these techniques we sharpen a result of Surányi [13] by showing that if an -critical graph has defect and contains nodes of degree , then the graph is an odd subdivision of .

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Received October 23, 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lipták, L., Lovász, L. Critical Facets of the Stable Set Polytope. Combinatorica 21, 61–88 (2001). https://doi.org/10.1007/s004930170005

Download citation

  • AMS Subject Classification (2000) Classes:  05C69; 90C57