Hoa's Conjecture on Maximal Non-Hamiltonian Graphs

Precise statement

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.

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

ChatGPT

The declaration of AI use says ChatGPT assisted in developing and checking the constructions and proofs, with the author independently verifying all arguments.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint, not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-08-02

   arXiv:2608.00957 - Counterexamples to a conjecture of Hoa on maximal non-Hamiltonian graphs

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• 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.