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Brualdi's Question on Hamiltonicity of Interchange Graphs

Combinatorics · posed by Richard A. Brualdi, 1980 · solved

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Statement

The interchange graph G(R,S)G(R,S) has the (0,1)(0,1)-matrices with row sums RR and column sums SS as vertices, adjacent when they differ by a single 2×22\times 2 interchange. Brualdi asked whether G(R,S)G(R,S) is always Hamiltonian. It satisfies more: it is maximally Hamiltonian, Hamilton-laceable when bipartite and Hamilton-connected when not.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Jeffrey S. Baggett and Huiya Yan, using Claude, GPT, Codex

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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    ai assisted
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    The declaration says the computational search and verification programs and the Lean 4 formalization were developed with AI-assisted tools under author direction, and that no AI system is an author. The structural induction carrying the proof is the authors'.

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