Claimed ETH refutations yield first sub-exponential algorithm counting Hamiltonian cycles
xennygrimmato_ · x · 2026-10-28
Assuming the recent ETH refutation claims by OpenAI (openai/math) and Anthropic (anthropics/formal-math, posted Oct 26, still under expert review) hold, the number of Hamiltonian cycles in an n-vertex graph with O(n) edges can be computed exactly and deterministically in sub-exponential time—every prior algorithm was exponential. The accompanying open-source paper gives the sharper rate 2^{O(n/sqrt(log n))}, matching the new SAT algorithms, and the sub-exponential bound is machine-checked in Lean on top of rebuilt versions of both labs' proofs. Results are conditional and sparse-graph only.
Related event: Subexponential Hamiltonian Cycle Algorithm Built on ETH Refutation(3 posts)→
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