Remark: Family 162. Counterexamples to Ryser's covering and Gyárfás's tree-cover conjectures

Disproves Ryser's covering conjecture by constructing intersecting $(q+1)$-partite, $(q+1)$-uniform hypergraphs with covering number $q+1$, rather than the predicted bound $q$, for every sufficiently large prime $q$. A separate construction over extension fields also disproves Gyárfás's monochromatic tree-cover conjecture.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.