We establish a general computational framework for Chvátal’s conjecture based on exact rational integer programming. As a result we prove Chvátal’s conjecture holds for all downsets whose union of sets contains seven elements or less. The computational proof relies on an exact branch-and-bound certificate that allows for elementary verification and is independent of the integer programming solver used.
August 2018, ZIB-Report 18-49, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany
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