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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.
Manuscripts in this family · 2
Balanced counterexamples to Ryser's conjecture at prime orders
Sep 27, 2026·paper.pdf
For every sufficiently large prime q, we construct a finite intersecting -partite -uniform hypergraph with covering number and exactly nonisolated vertices in each part. This disproves Ryser's covering conjecture, even for intersecting hypergraphs with equally sized parts.
A counterexample to Ryser's covering conjecture
Sep 23, 2026·paper.pdfLean
For every sufficiently large prime and every sufficiently large odd integer n, with the threshold depending on s, we construct an intersecting -partite -uniform hypergraph with covering number . This disproves Ryser's covering conjecture in its intersecting case.