number of spanning trees, asymptotics


Minimal graphs with a prescribed number of spanning trees ★★

Author(s): Azarija; Skrekovski

\begin{conjecture} Let $n \geq 3$ be an integer and let $\alpha(n)$ denote the least integer $k$ such that there exists a simple graph on $k$ vertices having precisely $n$ spanning trees. Then $ \alpha(n) = o(\log{n}).$ \end{conjecture}

Keywords: number of spanning trees, asymptotics

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