Abstract
Let c(n) be the maximum number of cycles in an outerplanar graph with n vertices. We show that lim c(n)1/n exists and equals β = 1.502837 . . ., where β is a constant related to the recurrence \({x_{n+1} = 1 + x_n^2, \, x_0=1}\). The same result holds for the larger class of series–parallel graphs.
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de Mier, A., Noy, M. On the Maximum Number of Cycles in Outerplanar and Series–Parallel Graphs. Graphs and Combinatorics 28, 265–275 (2012). https://doi.org/10.1007/s00373-011-1039-9
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DOI: https://doi.org/10.1007/s00373-011-1039-9