A counterexample to Ryser's covering conjecture
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.
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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…