Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 162-02. A counterexample to Ryser's covering conjecture
Manuscript map · lines 5465–5474
OpenAI@2026-10-07#rem:oai-p-162-02
Authors: OpenAI. Family 162.
Title: A counterexample to Ryser's covering conjecture.
Abstract: For every sufficiently large prime $s{}equiv2{}pmod3$ and every sufficiently large odd integer n, with the threshold depending on s, we construct an intersecting $(s{}n+1)$-partite $(s{}n+1)$-uniform hypergraph with covering number $s{}n+1$. This disproves Ryser's covering conjecture in its intersecting case.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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