Pavez-Signe's Length-Control Question for Spanning Subdivisions
Pavez-Signe (2024) conjectured a Dirac-type condition for spanning -subdivisions and asked whether the subdivision paths can additionally be required to have similar lengths; Lee (2025) resolved the existence conjecture in the stronger digraph setting. Answered affirmatively with epsilon-room: for every there is such that every -vertex digraph with and minimum semi-degree contains a spanning -subdivision whose path lengths differ by at most one, for every digraph with arcs and no isolated vertices.
- Result
- Proved
- Status
- Partial result
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Extremal graph theory - digraphs
- Posed by
- Matias Pavez-Signe
- Year posed
- 2024
- Years open
- 2y
- Solved
- 2026-08-14
- Model
- ChatGPT 5.6
- Vendor
- OpenAI
- Collaborators
- Zhilan Wang, Shuo Wei, Jin Yan
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 8 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgement states the authors used ChatGPT 5.6 to assist in the development of the probabilistic partition argument in one named lemma, plus language polishing, with all arguments independently verified by the authors.
Verification
Checked by this site on 17 August 2026 against the paper's LaTeX (arXiv:2608.14432, Wang-Wei-Yan): the attribution chain (Pavez-Signe's conjecture and question, Lee's resolution of existence) is in the abstract, the answer carries an epsilon in the semi-degree threshold rather than the exact conjectured bound - hence Partial, and the paper's own closing question asks for the exact threshold - and the AI acknowledgement is verbatim as quoted. Not checked here; days old, no independent review.