HEXAGONbeta

Hilton’s conjecture on cycle multiplicities

A mix of human-written and AI-generated textHuman understanding: some partsmath.CO — Combinatorics

Contributed by Qiyue Tang ↗

Version 1 / Nov 03, 2026 / CC BY 4.0

Abstract

We prove Hilton’s conjecture on the number of cycles of each length in dense Hamiltonian graphs. This resolves the problem posed by A. J.W. Hilton and recorded by Sheehan in 1977.

Provenance statement

The research reported here was developed in a ChatGPT-6-Pro conversation in approximately 56 minutes; the recorded session, including organization and delivery checks, lasted approximately 74 minutes. Codex was used for adversarial review and expository revision. The proof has passed an external Rethlas-OSV review .

References

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Version history

  1. v1 · 9 pagesSubmitted by Qiyue TangInitial depositCurrentNov 02, 2026