The node multiterminal cut polyhedron

Abstract

Given an undirected graph G = (V U A, E), where A is a set of terminal nodes and V is a set of nonterminal nodes, a node multiterminal cut is a set of nonterminal nodes whose deletion disconnects every pair of terminal nodes. We study the node multiterminal cut polyhedron, denoted P(G, A). We give some general results concerning facets of P(G, A) and introduce several classes of facet-inducing inequalities. We focus on the so-called A-tree inequalities (a generalization of the well-known path inequalities) and show that if G is a tree then these inequalities give a complete description of P(G, A). Assuming that the number of terminal nodes in an A-tree is O(1) or G is a tree, we give efficient separation algorithms for the A-tree inequalities.