Graffiti's Residue Problem for Common-Divisor Graphs
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.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Graph theory
- Posed by
- Graffiti (S. Fajtlowicz's program); studied by Erdős and Staton
- Year posed
- —
- Years open
- —
- Solved
- 2026-08-03
- Model
- Theo-Conjecture, OpenAI Codex
- Vendor
- —
- Collaborators
- Randy Davila
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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.