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Research questionHow can computational systems discover graph-theoretic conjectures that survive refutation and admit machine-checked proofs?Automated discovery must separate genuinely new conjectures from relations already implied by known results and expose candidates that fail on graphs or targeted searches. Candidates that survive those tests still need precise formal statements and proofs accepted by a trusted kernel.
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Latest papersRecent research connected to this question, newest first.AutoGraphForge: Towards Automated Graph Theory DiscoveryThe source describes Graffiti3 conjecture generation over an evolving graph-invariant table, novelty filtering against 559 known relations via linear programming, testing on roughly 348,000 graphs and several graph families, and additional counterexample searches on an HPC cluster. Surviving conjectures are translated into Lean 4 statement skeletons and checked against pinned mathlib4 and a custom invariant preamble, with DeepSeek-Prover-V2-671B and OProver-32B supplying candidate proofs; the full pipeline is reported as ongoing and initial sanity checks have passed.research paper · Sep 3, 2026
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