Ryser's conjecture on covers of r-partite hypergraphs

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Companion: Balanced counterexamples to Ryser's conjecture at prime orders (September 27, 2026) evidence for this event

This event attributed to Unreleased internal OpenAI model

VibeMathed record: Ryser's conjecture on covers of r-partite hypergraphs evidence for this event

Lean proof: OAI/Combinatorics/Ryser/OddExtensions.lean evidence for this event

Best and Wanless, What did Ryser conjecture? (arXiv:1801.02893) evidence for this event

Ryser's conjecture on covers of r-partite hypergraphs parent of this event

Gyarfas's conjecture on covering edge-colored complete graphs by r-1 monochromatic trees evidence for this event

Ryser's conjecture is false, already for intersecting hypergraphs. September 23: for every sufficiently large prime $s\equiv2\pmod3$ and every sufficiently large odd $n$ (threshold depending on $s$), there is an intersecting $(s^n+1)$-partite $(s^n+1)$-uniform hypergraph with $\tau=s^n+1$, against the conjectured $s^n$. September 27: for every sufficiently large prime $q$, an intersecting $(q+1)$-partite $(q+1)$-uniform hypergraph with $\tau=q+1$ and exactly $q+1$ nonisolated vertices in each part. Not given: an explicit rank or example, or anything for small $r$ (cases $r=4,5$ remain open in general). parent of this event

Lean proof (balanced companion): OAI/Combinatorics/BalancedRyser/Main.lean evidence for this event

Lean proof: OAI/Combinatorics/Ryser/Construction/Main.lean evidence for this event