OFFSET
1,2
COMMENTS
Heuberger and Wagner consider the number of maximum matchings a tree of n vertices may have. They show that the largest number of maximum matchings (A333347) grows as O(1.3916...^n) where the power is the constant here. This arises in their tree forms since each 7-vertex "C" part increases the number of matchings by a factor of matrix M=[8,3/5,3] (lemma 6.2). The larger eigenvalue of M is their lambda = A333345 and so a factor of lambda for each 7 vertices.
LINKS
Clemens Heuberger and Stephan Wagner, The Number of Maximum Matchings in a Tree, Discrete Mathematics, volume 311, issue 21, November 2011, pages 2512-2542; arXiv preprint, arXiv:1011.6554 [math.CO], 2010.
EXAMPLE
1.39166428413...
MATHEMATICA
RealDigits[((11 + Sqrt[85])/2)^(1/7), 10, 100][[1]] (* Amiram Eldar, Mar 15 2020 *)
PROG
(PARI) ((11 + sqrt(85))/2)^(1/7) \\ Stefano Spezia, Feb 09 2025
CROSSREFS
KEYWORD
AUTHOR
Kevin Ryde, Mar 15 2020
STATUS
approved