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WOWII Conjecture 72: Two induced trees pin down tree( $G$ )

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.

Exact FrontierDelta

proved→proved

Scope and record

Occurred: Oct 29, 2026

Delta type: REGISTRY REVISION

Assumptions: VibeMathed verification: site-confirmed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: WOWII Conjecture 72: Two induced trees pin down tree($ G $) · WOWII 72 (tree($ G $) bound)

Confidence: Not scored

Registry verification: site confirmed · announcement · candidate

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VibeMathed
registry · event recorded by

GPT 5.6 Sol
model · ai model contributor · OpenAI

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Named evidence

VibeMathed record: WOWII Conjecture 72: Two induced trees pin down tree( $G$ )

specialist registry · passed

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.

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WOWII Conjecture 72: Two induced trees pin down tree( $G$ )

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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WOWII Conjecture 72: Two induced trees pin down tree( $G$ ) evidence for this event

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This event attributed to GPT 5.6 Sol

VibeMathed record: WOWII Conjecture 72: Two induced trees pin down tree( $G$ ) evidence for this event

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