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The Demyanov-Ryabova conjecture is false. (English) Zbl 1417.90147
Summary: It was conjectured by V. F. Demyanov and J. A. Ryabova [Discrete Contin. Dyn. Syst. 31, No. 4, 1273–1292 (2011; Zbl 1254.90223)] that the minimal cycle in the sequence obtained via repeated application of the Demyanov converter to a finite family of polytopes is at most two. We construct a counterexample for which the minimal cycle has length 4.

MSC:
90C35 Programming involving graphs or networks
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