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Graffiti Conjecture 284

Combinatorics · posed by Graffiti (Siemion Fajtlowicz's program), 1996 · disproved

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Statement

If a finite graph has girth at least five, must its minimum dual degree satisfy δ∗(G)≤−∂n(G)\delta^*(G) \le -\partial_n(G), where ∂n(G)\partial_n(G) is the smallest eigenvalue of its distance matrix? The Hoffman-Singleton graph violates it: dual degree 77 against eigenvalue bound 44.

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

  1. construction · #1

    Grok 4.5 Medium (Capy build)

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    The Capy agent running Grok 4.5 Medium identified the Hoffman-Singleton graph as a counterexample; the certificate was reproduced independently under adversarial review.

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