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Tournaments Determined by Three and Five Voters

Combinatorics · posed by Milosz, Hamel and Pierrot; Shepard · disproved

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Statement

Around the Kemeny median problem, which stays open for m=3m=3 and m=5m=5 voters, the paper refutes three conjectures on tournament inducibility: both conjectures of Milosz, Hamel and Pierrot (the 3-cycle extension for odd m≥5m\ge5, and FAS=HS3\mathrm{FAS}=\mathrm{HS}_3 at n=11n=11), and Shepard's threshold conjecture.

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  1. construction · #1

    Leonid Chindelevitch and Ararat Harutyunyan, using Claude

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