Abstract
Given a complete graph K n on n nodes and a subset S of nodes, the cut δ( S) defined by S is the set of edges of K n with exactly one endnode in S. A cut δ( S) is an equicut if |S|=⌊ n 2 ⌋ or ⌈ n 2 ⌉ and an inequicut, otherwise. The cut cone C n (or inequicut cone IC n ) is the cone generated by the incidence vectors of all cuts (or inequicuts) of K n . The equicut polytope EP n , studied by Conforti et al. (1990), is the convex hull of the incidence vectors of all equicuts. We prove that IC n and EP n ‘inherit’ all facets of the cut cone C n , namely, that every facet of the cut cone C n yields (by zero-lifting) a facet of the inequicut cone IC m for n<⌊ m 2 ⌋ and of EP m for m odd, m⩾2 n+1. We construct several new classes of facets, not arising from C n , for the inequicut cone IC n and we describe its facial structure for n⩽7.
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