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- W2998994549 abstract "For n≥3, let r=r(n)≥3 be an integer. A hypergraph is r-uniform if each edge is a set of r vertices, and is said to be linear if two edges intersect in at most one vertex. In this paper, the number of linear r-uniform hypergraphs on n→∞ vertices is determined asymptotically when the number of edges is m(n)=o(r−3n3/2). As one application, we find the probability of linearity for the independent-edge model of random r-uniform hypergraph when the expected number of edges is o(r−3n3/2). We also find the probability that a random r-uniform linear hypergraph with a given number of edges contains a given subhypergraph." @default.
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- W2998994549 date "2020-04-01" @default.
- W2998994549 modified "2023-09-24" @default.
- W2998994549 title "Asymptotic enumeration of linear hypergraphs with given number of vertices and edges" @default.
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- W2998994549 doi "https://doi.org/10.1016/j.aam.2020.102000" @default.
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