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• W2955442955 abstract "Galled trees are studied as a recombination model in theoretic population genetics. This class of phylogenetic networks has been generalized to tree-child networks, normal networks and tree-based networks by relaxing a structural condition. Although these networks are simple, their topological structures have yet to be fully understood. It is well-known that all phylogenetic trees on $n$ taxa can be generated by the insertion of the $n$-th taxa to each edge of all the phylogenetic trees on $n-1$ taxa. We prove that all tree-child networks with $k$ reticulate nodes on $n$ taxa can be uniquely generated via three operations from all the tree-child networks with $k-1$ or $k$ reticulate nodes on $n-1$ taxa . An application of this result is found in counting tree-child networks and normal networks. In particular, a simple formula is given for the number of rooted phylogenetic networks with one reticulate node." @default.
• W2955442955 created "2019-07-12" @default.
• W2955442955 creator A5012300835 @default.
• W2955442955 date "2019-06-28" @default.
• W2955442955 modified "2023-09-26" @default.
• W2955442955 title "Generating Normal Networks via Leaf Insertion and Nearest Neighbor Interchange" @default.
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• W2955442955 doi "https://doi.org/10.48550/arxiv.1906.12053" @default.
• W2955442955 hasPublicationYear "2019" @default.
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