Facets of the K-partition Polytope

We study facets of the k-partition polytope Pk.+, the convex hull of edges cut by r-partitions of a complete graph for r < k, k 2 3. We generalize the hypermetric and cycle inequalities (see Deza and Laurent, 1992) from the cut polytope to Pk.,, k 2 3. We give some sufficient conditions under which these are facet defining. We show the anti-web inequality introduced by Deza and Laurent (1992) to be facet defining for Pi,_, k 2 3. We also give lifting procedures for constructing facets of Pk., from facets of P k,n for r 2 n + 1 and facets of Pk.r from facets of Pk_l.n for r > n + 1. Kevwords: k-partition polytope; Valid inequality; Facet; Lifting