A bound on the k-gonality of facets of the hypermetric cone and related complexity problems

Abstract

We give a bound on gh(n), the largest integer such that there is a gh(n)-gonal facet of the hypermetric cone Hypn, gh(n) ≤ 2n-2 (n-1)! This proves simultaneously the polyhedrality of the hypermetric cone. We give complete description of Delaunay polytopes related to facets of Hypn. We prove that the problem determining hypermetricity lies in co-NP and give some related NP-hard problem. © 1993.