WOWII Conjecture 72: Two induced trees pin down tree($ G $)
candidateconfidence 50%
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
For a connected graph $ G $, let $ t= $ tree($ G $) (order of a largest induced tree), $ A= $ average eccentricity, and $ L= $ maximum independence number of a neighbourhood. Then
$ \lceil (A+L)/3 \rceil \le t. $
(The evenly-divided reading of the conjecture holds; a stronger reading that divides only $ L $ by three is false.)
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
GPT 5.6 Sol
The model was given a short prompt (copied from a successful earlier run on a different WOWII conjecture) and asked to find a solution or counterexample to an open conjecture of its choosing. It selected WOWII Conjecture 72, produced the two-lemma argument (diametral path induces a tree on $ D+1 $ vertices; maximum independent neighbourhood induces a star on $ L+1 $ vertices), derived the bound $ \lceil(A+L)/3\rceil\le t $, and explicitly distinguished the evenly-divided reading (true) from the stronger reading that divides only $ L $ by three (false). The human then posted the diagram and commentary.
Re-derived in full by this site on 17 August 2026 - the argument is elementary and correct, and short enough to state: a shortest path between two vertices at maximum distance D is induced, so it induces a path (a tree) on D+1 vertices, giving tree(G) >= D+1 >= A+1 since average eccentricity is at most D; a maximum independent set in a neighbourhood plus its centre induces a star on L+1 vertices, giving tree(G) >= L+1; hence A + L <= 2*tree(G) - 2, and ceil((A+L)/3) <= tree(G) follows by integrality. The stronger reading (dividing only L by three) fails on the claimed counterexample family. What keeps this Candidate is not the mathematics but the statement: Conjecture 72's canonical wording is not publicly pinned (no formal statement exists in the Formal Conjectures repository), so which reading DeLaViña intended is unconfirmed, and the X post plus transcript is the only artifact. Site-confirmed records this site's independent re-derivation of the proved reading.
X post by @4thRT (with attached diagram and ChatGPT conversation link)
The evenly-divided reading of WOWII Conjecture 72 holds:
$ \lceil(A + L)/3\rceil \le t, $
where $ t = $ tree($ G $) (order of a largest induced tree), $ A = $ average eccentricity and $ L = $ maximum neighbourhood independence number.
A stronger reading that divides only $ L $ by three is false. The argument rests on two elementary observations (a diametral path is chordless and therefore induces a tree on $ D+1 $ vertices; a maximum independent set in a neighbourhood induces a star on $ L+1 $ vertices). The original conjecture’s precise wording is not yet pinned in a public formal repository, so statement fidelity remains to be audited.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
The source status is candidate and must not be represented as solved.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.