Combinatorics · Oct 6, 2026
Counterexamples to Ryser’s covering conjecture
Disproves Ryser's covering conjecture by constructing intersecting -partite, -uniform hypergraphs with covering number , rather than the predicted bound q, for every sufficiently large prime q. A separate construction over extension fields also disproves Gyárfás's monochromatic tree-cover conjecture.
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