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number of spanning trees, asymptotics


Graph Theory

Minimal graphs with a prescribed number of spanning trees ★★

Author(s): Azarija; Skrekovski

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}). $

Keywords: number of spanning trees, asymptotics

Posted by azi
updated April 22nd, 2012
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