The k-node-connected subgraph problem: Facets and Branch-and-Cut

Abstract

In this paper we consider the k-node-connected subgraph problem. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We introduce further classes of valid inequalities and discuss their facial aspect. We also devise separation routines and discuss some structure properties and reduction operations. Using these results, we devise a Branch-and-Cut algorithm along with some computational results.