The enumeration problem for color critical linear hypergraphs

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Abstract

Denote by S(m, n, r) the number of non-isomorphic r-critical linear n-graphs on m vertices. It is shown that for n ≥ 3, r ≥ 3 there exists a constant c > 1 depending only on n and r such that S(m, n, r) > cm for all sufficiently large m.

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