Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-10-16 , DOI: 10.1016/j.disc.2020.112192
Haya S. Aldosari; Catherine Greenhill

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 et al. (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 $\mathbit{k}=\left({k}_{1},\dots ,{k}_{n}\right)$. Our formula holds when ${r}^{5}{k}_{\mathrm{max}}^{3}=o\left(\left(kr-k-r\right)n\right)$, where $k$ is the average degree and ${k}_{\mathrm{max}}$ is the maximum degree.

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