On the number of spanning trees in random regular graphs
arXiv preprint arXiv:1309.6710, 2013•arxiv.org
Let $ d\geq 3$ be a fixed integer. We give an asympotic formula for the expected number of
spanning trees in a uniformly random $ d $-regular graph with $ n $ vertices.(The
asymptotics are as $ n\to\infty $, restricted to even $ n $ if $ d $ is odd.) We also obtain the
asymptotic distribution of the number of spanning trees in a uniformly random cubic graph,
and conjecture that the corresponding result holds for arbitrary (fixed) $ d $. Numerical
evidence is presented which supports our conjecture.
spanning trees in a uniformly random $ d $-regular graph with $ n $ vertices.(The
asymptotics are as $ n\to\infty $, restricted to even $ n $ if $ d $ is odd.) We also obtain the
asymptotic distribution of the number of spanning trees in a uniformly random cubic graph,
and conjecture that the corresponding result holds for arbitrary (fixed) $ d $. Numerical
evidence is presented which supports our conjecture.
Let be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random -regular graph with vertices. (The asymptotics are as , restricted to even if is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) . Numerical evidence is presented which supports our conjecture.
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