Not evaluated
Maximum number of Hamiltonian cycles in a tournament: announced proof of a conjecture of Wormald (Divoux and Wang, with GPT-5.6)
The gist
On October 16, 2026, Alexander Divoux and Shouda Wang posted on arXiv the asymptotic value of the maximum number of Hamiltonian cycles in a tournament, which would prove a conjecture of Wormald, from proofs found by GPT-5.6.
DiscoverIA status on October 24, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 24, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 24, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-divoux-wang-cycles-hamiltoniens-2026-10-16-r1
@misc{discoveria-divoux-wang-cycles-hamiltoniens-2026-10-16-r1,
author = {{DiscoverIA}},
title = {Maximum number of Hamiltonian cycles in a tournament: announced proof of a conjecture of Wormald (Divoux and Wang, with GPT-5.6)},
howpublished = {DiscoverIA registry, entry divoux-wang-cycles-hamiltoniens-2026-10-16},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/divoux-wang-cycles-hamiltoniens-2026-10-16#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A tournament is a graph in which every pair of vertices is joined by an arrow in one direction only; a Hamiltonian cycle passes once through every vertex along the arrows. If the result held, the maximum number of such cycles would be known asymptotically, with the constant cosh 1 / cos 1, proving a conjecture of Wormald and answering a question of Noga Alon.
What remains unclear
The 49-page paper has not yet been peer-reviewed or formalised. According to the authors, many of GPT-5.6's arguments were later replaced or simplified by them, and others came from the literature. A stronger conjecture of Wormald, that one specific tournament attains the exact maximum for all large enough odd n, remains open.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.23755
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What this status means
Source reading : Source read word for word (level 3 of 3)
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To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcearxiv.org · abs/2610.23755page read word for word · consulted on Oct 24, 2026 ·
This answers a question of Alon and proves a conjecture of Wormald.
- Paperarxiv.org · html/2610.23755page read word for word · consulted on Oct 24, 2026 ·
We provide our own exposition of these proofs, which were originally found by GPT-5.6.
Method
GPT-5.6 found a proof of the lower bound following strategies supplied by the authors (searching for suitable permanent estimates), and a separate instance of the model then generalised its techniques into an argument for the matching upper bound. The result reads C(n) = (cosh 1 / cos 1 ± o(1)) (n−1)!/2^n; Jay Pantone had guessed the constant numerically. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 24, 2026 from arxiv.org (page read, quotation checked word for word: “This answers a question of Alon and proves a conjecture of Wormald.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- Alexander Divoux et Shouda Wang, with GPT-5.6 (OpenAI)
announced on Oct 16, 2026 - Nature
- new result
- Field
- Mathematics (combinatorics / tournaments)
- Checked by
- no verifier identified
- Sources
- 2 : 2 read word for word
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
arXiv preprint, not peer-reviewed or formalised; proofs rewritten by the authors; no third-party evaluation found
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
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