What was already known
Gyárfás conjectured that r−1 monochromatic trees always suffice. Earlier counterexamples to a tree-partition statement did not settle this covering question.
AI involvement
The graph corollary transfers OpenAI’s model-produced hypergraph construction. No named human check or explanation of the transfer is documented.
The graph corollary transfers the model-produced Ryser construction; the release credits the internal model and does not document autonomy.
Importance
The construction would refute the separate monochromatic tree-cover conjecture at the stated ranks.
Limitations
The graph statement is a corollary of the same hypergraph construction used for the odd-extension Ryser result. Lean checks the hypergraph premise, while the graph transfer has no documented completed check.
Technical verification
The source-reported Lean proof covers the underlying finite intersecting hypergraph and its cover number. The graph-coloring transfer in Corollary 1.2 is written in the manuscript but has no documented completed human or machine check, so Formal is not assigned to the full graph claim.
Formal checking
Lean proof of the hypergraph premise used by the graph corollary
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- Finite intersecting r-partite hypergraphs with matching number one and cover number r at eventual odd-extension ranks, used as the graph corollary's premise
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The OpenAI-authored manuscript presents the elementary transfer, but no named human explanation of the underlying construction is documented. Few is the evidence default.
Correction and publication history
The construction would refute the separate monochromatic tree-cover conjecture at the stated ranks.
Read this published revision