Balanced counterexamples to Ryser's conjecture at prime orders
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.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
to meet every edge, whereas the conjecture predicts . Crossing numbers of complete and complete bipartite graphs. These problems appeared in my discussion of Turán’s mathematics . The release reports proofs of the Harary–Hill and Zarankiewicz formulas, determining the minimum number of crossings…