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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.

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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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  1. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols & Dabeen Lee

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  1. Gérard Cornuéjols
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  2. Dabeen Lee
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Correspondence to Gérard Cornuéjols.

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Cornuéjols, G., Lee, D. On some polytopes contained in the 0, 1 hypercube that have a small Chvátal rank. Math. Program. 172, 467–503 (2018). https://doi.org/10.1007/s10107-017-1226-4

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  • DOI: https://doi.org/10.1007/s10107-017-1226-4

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