The optimal k-restricted 2-factor problem consists of finding, in a complete undirected graph Kn, a minimum cost 2-factor (subgraph having degree 2 at every node) with all components having more than k nodes. The problem is a relaxation of the well-known symmetric travelling salesman problem, and is equivalent to it when n/2 ≤ k ≤ n − 1. We study the k-restricted 2-factor polytope. We present a large class of valid inequalities, called bipartition inequalities, and describe some of their properties; some of these results are new even for the travelling salesman polytope. For the case k = 3, the triangle-free 2-factor polytope, we derive a necessary and sufficient condition for such inequalities to be facet inducing.
