The signature of a connected line graph is at most 1 (Akbari, Elphick, Kumar, Pragada, Tang, Discrete Math. 349 (2026) 114953, Conjecture 4.12).
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Assessment
Renown 2/5
A 2026 conjecture from a published Discrete Mathematics paper; specialist renown.
Attackability 4/5
Cheap eigendecomposition oracle, equality cases as seeds; refuted within a year of publication.
- finite witness
- 5/5
- oracle cost
- 5/5
- freshness
- 4/5
- seedability
- 4/5
Confirmed resolution
counterexample by Andrea Paone (Zenodo, 2026-07-22); Luke Francis and Trevor Uptain (arXiv, submitted 2026-07-24) on .
Independent contemporaneous discoveries of the same 14-vertex graph (isomorphism machine-verified). First public evidence: Paone, Zenodo V1, 2026-07-22, with unboundedness in V2 (2026-07-24) via a rooted-module route. Francis and Uptain proved unboundedness independently via a bridge lemma (signature k+1 on 14k vertices), arXiv:2607.22874 (submitted 2026-07-24, announced 2026-07-27); they state, and the source paper's authors can corroborate, that the 14-vertex example was communicated privately to those authors on 2026-07-20 and the unbounded family in correspondence of 2026-07-21 to 23. The source paper's authors additionally report receiving further independent copies of the same graph. Disclosure: this entry concerns work by the Board's operator. All edits are logged in the public status history, and the entry text was shared with all named parties for accuracy review.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
Confirmed
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