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Graffiti's Residue Problem for Common-Divisor Graphs

Combinatorics · posed by Graffiti (S. Fajtlowicz's program); studied by Erdős and Staton · solved

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Statement

A problem from Fajtlowicz's Graffiti program, studied by Erdős and Staton, on the Havel-Hakimi residue of common-divisor graphs. The paper resolves the problem and extends it, determining the residue's first-order scale and its nontrivial constant from the degree sequence.

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

  1. proof attempt · #1

    Randy Davila, using Theo-Conjecture, OpenAI 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.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The study deliberately retained Graffiti's conjecture-example-proof workflow through the TxGraffiti / Theo-Conjecture line: the systems supported registry construction, conjecture generation, exact stress testing, proof search and proof auditing, with the surviving conjecture selected by discrepancy tracking against a quarter-million-graph registry.

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