Counting cherry reduction sequences is counting linear extensions (in phylogenetic tree-child networks)

Tomás M. Coronado; Joan Carles Pons; Gabriel Riera

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arXiv · 2403.14491

Counting cherry reduction sequences is counting linear extensions (in phylogenetic tree-child networks)

Tomás M. Coronado·Joan Carles Pons·Gabriel Riera

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Abstract

Orchard and tree-child networks share an important property with phylogenetic trees: they can be completely reduced to a single node by iteratively deleting cherries and reticulated cherries. As it is the case with phylogenetic trees, the number of ways in which this can be done gives information about the topology of the network. Here, we show that the problem of computing this number in tree-child networks is akin to that of finding the number of linear extensions of the poset induced by each network, and give an algorithm based on this reduction whose complexity is bounded in terms of the level of the network.

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Tomás M. Coronado, Joan Carles Pons, Gabriel Riera. 2024-03-21. Counting cherry reduction sequences is counting linear extensions (in phylogenetic tree-child networks). https://arxiv.org/abs/2403.14491

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