On some polytopes contained in the 0, 1 hypercube that have a small Chvátal rank

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Abstract

In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of 0, 1 vectors not contained in P that guarantee that P has a small Chvátal rank. Our conditions are in terms of the subgraph induced by these infeasible 0, 1 vertices in the skeleton graph of the unit hypercube. In particular, we show that when this subgraph contains no 4-cycle, the Chvátal rank is at most 3; and when it has tree width 2, the Chvátal rank is at most 4. We also give polyhedral decomposition theorems when this graph has a vertex cutset of size one or two.

Mathematics Subject Classification

90C10 90C27 90C57 

Notes

Acknowledgements

This work was supported in part by NSF Grant CMMI1560828 and ONR Grant N00014-15-12082. We would like to thank the referees for carefully reading an earlier draft of the paper and providing valuable comments.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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