For every sufficiently large prime q, a finite intersecting (q+1)-partite (q+1)-uniform hypergraph has covering number q+1 and exactly q+1 nonisolated vertices in each part.
For every sufficiently large prime q, a finite intersecting (q+1)-partite (q+1)-uniform hypergraph has covering number q+1 and exactly q+1 nonisolated vertices in each part.
For every sufficiently large prime q, a finite intersecting (q+1)-partite (q+1)-uniform hypergraph has covering number q+1 and exactly q+1 nonisolated vertices in each part.
If correct, disproves Ryser’s covering conjecture even with equal-sized vertex parts.
Can an intersecting r-partite hypergraph require r vertices to cover despite Ryser’s conjectured r−1 bound?
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OpenAI reports balanced counterexamples to Ryser’s covering conjecture
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