AI Agent's Systematic Attack on Conway's 99-Graph Problem
A recent preprint on arXiv (2608.11211) details a comprehensive and reproducible assault on Conway's 99-graph challenge, which inquires about the existence of a strongly regular graph with parameters srg(99,14,1,2). This research was performed by an autonomous AI agent and scored using a partial-credit metric. Key contributions of the paper include: (1) a complete proof demonstrating that no circulant graph on Z/99 meets more than 3366/4950 = 68.0% of the requirements (33 out of 49 difference-classes), which holds true for the other abelian group of order 99; (2) a forced-structure reduction leading to a 12-regular graph on 84 vertices; (3) a validated framework for prescribed-automorphism orbit existence. This work represents a significant step in applying AI to a long-standing graph theory problem, although it remains preliminary and has yet to undergo peer review. The paper can be accessed at https://arxiv.org/abs/2608.11211.
Key facts
- The paper addresses Conway's 99-graph problem, asking if a strongly regular graph srg(99,14,1,2) exists.
- An autonomous AI research agent conducted the attack, scored under a partial-credit metric.
- Exhaustive proof: no circulant graph on Z/99 satisfies more than 68.0% of constraints (33 of 49 difference-classes).
- The same ceiling applies to the other abelian group of order 99.
- Forced-structure reduction: λ=1 makes each neighbourhood a perfect matching; μ=2 puts outer vertices in bijection with non-matched neighbour-pairs.
- The reduction collapses existence to a 12-regular graph on 84 vertices, encoded for CP-SAT.
- The reduction was validated by recovering the unique srg(9,4,1,2).
- A validated prescribed-automorphism orbit-existence framework was developed, including fixed-point-free and single-fixed-point actions, checked on known graphs.
- The paper is a new arXiv preprint (2608.11211), not yet peer-reviewed.
Entities
Institutions
- arXiv