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. 2024 May 18;86(7):76.
doi: 10.1007/s11538-024-01309-w.

Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks

Yu-Sheng Chang  1 , Michael Fuchs  2
Affiliations

Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks

Yu-Sheng Chang et al. Bull Math Biol. .

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.

Keywords: Component graph method; Enumeration; Galled network; Phylogenetic network; Reticulation-visible network.

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References

    1. Bordewich M, Semple C (2016) Reticulation-visible networks. Adv Appl Math 78:114–141 - DOI
    1. Cardona G, Zhang L (2020) Counting and enumerating tree-child networks and their subclasses. J Comput Syst Sci 114:84–104 - DOI
    1. Chang Y-S, Fuchs M, Liu H, Wallner M, Yu G-R (2022a) Enumeration of [Formula: see text]-combining tree-child networks, LIPICS. In: Proceedings of the 33rd meeting on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms, vol 225. p 5
    1. Chang Y-S, Fuchs M, Liu H, Wallner M, Yu G-R (2022b) Enumerative and distributional results for [Formula: see text]-combining tree-child networks. Adv Appl Math 157:102704
    1. Chang Y-S, Fuchs M, Yu G-R (2024) Galled tree-child networks, LIPICS. In: Proceedings of the 35th meeting on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms, vol 302. p 2

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