A Forced-Structure Reduction and Verifiable Bounds for Conway's 99-Graph
Autonomous agents push the boundaries of graph theory by identifying structural constraints in the 99-graph problem.
Conway's 99-graph problem asks whether a strongly regular graph with parameters $\mathrm{srg}(99,14,1,2)$ exists. We report a systematic, fully reproducible attack by an autonomous AI research agent, scored under the track's partial-credit metric. Our verifiable contributions are...
ArXiv CS.AI
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This research demonstrates how autonomous AI agents can systematically tackle long-standing problems in algebraic graph theory by combining formal verification with constrained search techniques. By establishing clear upper bounds on graph existence, the study bridges the gap between raw computational power and rigorous mathematical proof.
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