Cardinality constrained combinatorial optimization: Complexity and polyhedra
Discrete Optimization
Dual consistent systems of linear inequalities and cardinality constrained polytopes
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Characterization of facets of the hop constrained chain polytope via dynamic programming
Discrete Applied Mathematics
On cardinality constrained polymatroids
Discrete Applied Mathematics
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Given a directed graph D = (N, A) and a sequence of positive integers $${1 \leq c_1 D of cardinality c p for some $${p \in \{1,\ldots,m\}}$$, respectively. We present integer characterizations of these polytopes by facet defining linear inequalities for which the separation problem can be solved in polynomial time. These inequalities can simply be transformed into inequalities that characterize the integer points of the undirected counterparts of cardinality constrained path and cycle polytopes. Beyond we investigate some further inequalities, in particular inequalities that are specific to odd/even paths and cycles.