Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks
Yu-Sheng Chang1, Michael Fuchs2
1Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan.
Bulletin of Mathematical Biology
|May 18, 2024
Abstract:
We give exact and asymptotic counting results for the number of galled networks and reticulation-visible networks with few reticulation vertices. Our results are obtained with the component graph method, which was introduced by L. Zhang and his coauthors, and generating function techniques. For galled networks, we in addition use analytic combinatorics. Moreover, in an appendix, we consider maximally reticulated reticulation-visible networks and derive their number, too.
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