Problem detail · source-aware
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Tuza conjectured that every finite simple graph satisfies $\tau(G) \leq 2\nu(G)$, where $\nu$ counts pairwise edge-disjoint triangles and $\tau$ is the fewest edges whose deletion leaves the graph triangle-free. Puleo had proved it for maximum average degree below 7. Proved here for every graph of maximum degree at most seven, crossing the equality boundary of Puleo's sparsity theorem.
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.
Both were "used extensively for proof exploration, software development, exact computational checks, literature discovery, and drafting and editing the manuscript", with the author selecting the arguments and methods and checking the sources and computations. Broad rather than step-attributed, so the lower tier applies.
Provider: Anthropic, OpenAI · Prompt public: unknown · Independence: unknown
A preprint days old with no independent review. A certificate catalogue and verification programs ship as ancillary files and in a companion repository, so the computational part is reproducible.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Settles a class, not the conjecture: Tuza's conjecture remains open in general.
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.