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- W2959649007 abstract "An $r$-uniform hypergraph $H$ consists of a set of vertices $V$ and a set of edges whose elements are $r$-subsets of $V$. We define a hypertree to be a connected hypergraph which contains no cycles. A hypertree spans a hypergraph $H$ if it is a subhypergraph of $H$ which contains all vertices of $H$. Greenhill, Isaev, Kwan and McKay (2017) gave an asymptotic formula for the average number of spanning trees in graphs with given, sparse degree sequence. We prove an analogous result for $r$-uniform hypergraphs with given degree sequence $boldsymbol{k} = (k_1,ldots, k_n)$. Our formula holds when $r^5 k_{max}^3 = o((kr-k-r)n)$, where $k$ is the average degree and $k_{max}$ is the maximum degree." @default.
- W2959649007 created "2019-07-23" @default.
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- W2959649007 date "2019-07-11" @default.
- W2959649007 modified "2023-09-27" @default.
- W2959649007 title "The average number of spanning hypertrees in sparse uniform hypergraphs." @default.
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