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

2024/01/17 by Yu‐Sheng Chang, Chang, Yu-Sheng, Michael Fuchs +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #05A15 #92B05 #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Fractal and DNA sequence analysis #Genome Rearrangement Algorithms

paper · pdf · doi:10.48550/arxiv.2401.08958

openalex publication_date 2024/01/17 · openalex created_date 2024/01/19 · openalex updated_date 2026/07/28

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.

Related

• Counting Phylogenetic Networks with Few Reticulation Vertices: Tree-Child and Normal Networks
• Counting Phylogenetic Networks with Few Reticulation Vertices: Exact Enumeration and Corrections
• Counting General Phylogenetic networks
• Counting and Enumerating Galled Networks
• Asymptotic Enumeration and Distributional Properties of Galled Networks