Intersecting and $2$-intersecting hypergraphs with maximal covering number: the Erdős-Lovász theme revisited
János Barát
Abstract:Erdős and Lovász noticed that an r-uniform intersecting hypergraph H with maximal covering number, that is τ (H) = r, must have at least 8 3 r − 3 edges. There has been no improvement on this lower bound for 45 years. We try to understand the reason by studying some small cases to see whether the truth lies very close to this simple bound. Let q(r) denote the minimum number of edges in an intersecting r-uniform hypergraph. It was known that q(3) = 6 and q(4) = 9. We obtain the following new results: The extrem… Show more
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