On the Linear Description of the k‐cycle Polytope

Abstract

We study a linear description of PCkn the convex hull of incidence vectors of all the cycles consisting of exactly k edges (k≥4) in Kn, the complete undirected graph with n vertices. First, we describe some properties of PCkn. Second, we discuss relations between PCkn and PCk′n′ with k′>k and n′>n. Then we give three lifting algorithms that transform a facet of PCkn into facets of PCkn′ with n′>n. Finally, we provide an integer formulation and a partial linear description of PCkn.