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Skrekovski, Riste
Minimal graphs with a prescribed number of spanning trees ★★
Author(s): Azarija; Skrekovski
Conjecture Let
be an integer and let
denote the least integer
such that there exists a simple graph on
vertices having precisely
spanning trees. Then
![$ n \geq 3 $](/files/tex/03699c2971c6eb403dcc4c26a1c9818ad7b45da8.png)
![$ \alpha(n) $](/files/tex/7cf5e54f55a113042ef4e18f16bdf6601a27462e.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ \alpha(n) = o(\log{n}). $](/files/tex/196d4bae3ba249904f8319dc18b830afd9cc7fe8.png)
Keywords: number of spanning trees, asymptotics
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