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arXiv · 2609.25177

Characterization of tree-child networks in terms of mu vectors

Toni Fuentes·Vincent Moulton·Katharina T. Huber·Joan Carles Pons
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Abstract

We characterize tree-child phylogenetic networks in terms of their mu-representations. First, we give a structural characterization of tree-child networks by means of ordered tree-path decompositions. We then translate this decomposition into a set of purely vectorial conditions on finite subsets M in N^n. We prove that such a set M is the mu-representation of a tree-child phylogenetic network if and only if it is tree-child mu-compatible. This provides a feasibility criterion for tree-child mu-representations which can be used as a basis for reconstruction and further algorithmic applications. Note that this paper presents results arising from ongoing research on tree-child networks and that the results will be further developed and placed into proper context in subsequent versions.

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Toni Fuentes, Vincent Moulton, Katharina T. Huber, Joan Carles Pons. 2026-09-21. Characterization of tree-child networks in terms of mu vectors. https://arxiv.org/abs/2609.25177

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