A Note on Clique-Web Facets for Multicut Polytopes

In this note we provide a previously undiscovered necessary condition for the facet-defining property of clique-web inequalities for the multicut polytope. This condition imposes a minimum cardinality requirement on the node set of the clique, thus implying, in general, that clique-web inequalities associated with relatively small cliques are not facet-defining for multicut polytopes.