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- W4287333036 abstract "We prove the following sharp estimate for the number of spanning trees of a graph in terms of its vertex-degrees: a simple graph $G$ on $n$ vertices has at most $(1/n^{2}) prod_{v in V(G)} (d(v)+1)$ spanning trees. This result is tight (for complete graphs), and improves earlier estimates of Alon from 1990 and Kostochka from 1995 by a factor of about $1/n$ (for dense graphs). We additionally show that an analogous bound holds for the weighted spanning tree enumerator of a (nonnegatively) weighted graph as well." @default.
- W4287333036 created "2022-07-25" @default.
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- W4287333036 date "2021-02-02" @default.
- W4287333036 modified "2023-09-23" @default.
- W4287333036 title "Sharp estimates for spanning trees" @default.
- W4287333036 doi "https://doi.org/10.48550/arxiv.2102.01669" @default.
- W4287333036 hasPublicationYear "2021" @default.
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