On cardinality constrained polymatroids

This paper extends results on the cardinality constrained matroid polytope presented in Maurras and Stephan (2011) [8] to polymatroids and the intersection of two polymtroids. Given a polymatroid P-f(S) defined by an integer submodular function f on some set S and an increasing finite sequence c of natural numbers, the cardinality constrained polymatroid is the convex hull of the integer points x is an element of P-f(S) whose sum of all entries is a member of c. We give a complete linear description for this polytope, characterize some facets of the cardinality constrained version of P-f(S), and briefly investigate the separation problem for this polytope. Moreover, we extend the results to the intersection of two polymatroids. (C) 2011 Elsevier RV. All rights reserved.