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On Vertices and Facets of Combinatorial 2-Level Polytopes

  • Manuel AprileEmail author
  • Alfonso Cevallos
  • Yuri Faenza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9849)

Abstract

2-level polytopes naturally appear in several areas of mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics.

We investigate upper bounds on the product of the number of facets \(f_{d-1}(P)\) and the number of vertices \(f_0(P)\), where d is the dimension of a 2-level polytope P. This question was first posed in [3], where experimental results showed \(f_0(P)f_{d-1}(P)\le d 2^{d+1}\) up to \(d=6\).

We show that this bound holds for all known (to the best of our knowledge) 2-level polytopes coming from combinatorial settings, including stable set polytopes of perfect graphs and all 2-level base polytopes of matroids. For the latter family, we also give a simple description of the facet-defining inequalities. These results are achieved by an investigation of related combinatorial objects, that could be of independent interest.

Keywords

Perfect Graph Linear Description Cycle Space Binary Matroids Eulerian Subgraph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.École Polytechnique Fédérale de LausanneLausanneSwitzerland

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