The Espuny Diaz-Lichev-Wesolek Conjecture on Dirac Subgraphs
Espuny Diaz, Lichev and Wesolek conjectured that a Dirac-type minimum degree condition forces Hamiltonicity in spanning subgraphs of cycle powers. Asymptotically true: for every and all large , any spanning subgraph of the th power of a cycle with minimum degree at least has a Hamilton cycle.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Graph theory
- Posed by
- Alberto Espuny Diaz, Lyuben Lichev, Alexandra Wesolek
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-05
- Model
- ChatGPT 5.5 Pro
- Vendor
- OpenAI
- Collaborators
- Richard Lang, Alp Muyesser, Mathias Schacht, Carl Schneider
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
asymptotic in k; the paper also shows the analogous statement is false for d = 2
What the AI did
The credit is specific and negative-result shaped: the authors show the analogous statement fails for , and say the crucial construction behind that was suggested to them by ChatGPT 5.5 Pro, with a dedicated appendix discussing it.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2606.07471 - Dirac subgraphs of powers of cycles are Hamiltonian