Graffiti's Residue Problem for Common-Divisor Graphs
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.
Context
A machine-generated Graffiti conjecture, the band the scoring ladder pins at 5, though this one carries Erdős and Staton's names in its history.
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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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