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math.CO2026
A cube-root phase transition in tree-child networks and the enumeration threshold for galled networks
Michael Fuchs, Hao Yu
We prove two surprising results about phylogenetic networks. First, we show that the structure of tree-child networks with leaves and reticulation nodes undergoes a sharp p…
math.CO2024★ 1 cited
Galled Tree-Child Networks
Yu-Sheng Chang, Michael Fuchs, Guan-Ru Yu
We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asympto…
math.CO2024
Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks
Yu-Sheng Chang, Michael Fuchs
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…