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Hoa's Conjecture on Maximal Non-Hamiltonian Graphs

A graph $G$ is maximal non-Hamiltonian if it is non-Hamiltonian but $G + e$ is Hamiltonian for every nonedge $e$. In 1994 Vu Dinh Hoa conjectured a property of $G - V(C)$ for a longest cycle $C$ of such a graph. Disproved by an explicit base graph on 56 vertices, extended to larger orders.

Exact FrontierDelta

Prior state unknowndisproved

Scope and record

Occurred: Aug 2, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: Hoa's Conjecture on Maximal Non-Hamiltonian Graphs · Hoa's conjecture

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Xingzhi Zhan
human · human collaborator

ChatGPT
model · ai model contributor · OpenAI

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This event attributed to Xingzhi Zhan

This event attributed to ChatGPT

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Hoa's Conjecture on Maximal Non-Hamiltonian Graphs — Mathematical Frontier Network