Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 162-01. Balanced counterexamples to Ryser's conjecture at prime orders
Manuscript map · lines 5455–5464
OpenAI@2026-10-07#rem:oai-p-162-01
Authors: OpenAI. Family 162.
Title: Balanced counterexamples to Ryser's conjecture at prime orders.
Abstract: For every sufficiently large prime q, we construct a finite intersecting $(q+1)$-partite $(q+1)$-uniform hypergraph with covering number $q+1$ and exactly $q+1$ nonisolated vertices in each part. This disproves Ryser's covering conjecture, even for intersecting hypergraphs with equally sized parts.
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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