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Gerard Cornuejols(gc0vandrew.cmu.edu) 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 Chvatal 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 4cycle, the Chvatal rank is at most 3; and when it has tree width 2, the Chvatal rank is at most 4. We also give polyhedral decomposition theorems when this graph has a vertex cutset of size one or two. Keywords: Integer programming, Chvatal rank, Chvatal cuts Category 1: Integer Programming (01 Programming ) Category 2: Integer Programming ((Mixed) Integer Linear Programming ) Category 3: Integer Programming (Cutting Plane Approaches ) Citation: Mathematical Programming B, 2018 Download: [PDF] Entry Submitted: 08/07/2018 Modify/Update this entry  
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