Counting graphs with different numbers of spanning trees through the counting of prime partitions
classification
🧮 math.CO
keywords
sqrtcountingspanningtreesconnecteddifferentexistsfaster
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Let A_n (n >= 1) be the set of all integers x such that there exists a connected graph on n vertices with precisely x spanning trees. In this paper, we show that |A_n| grows faster than sqrt{n}exp(2Pi*sqrt{n/log{n}/Sqrt(3)} This settles a question of Sedlacek.
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