Characterization of tree-child networks in terms of mu vectors
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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BibTeX
@misc{fuentes2026characterization,
title = {{Characterization of tree-child networks in terms of mu vectors}},
author = {Toni Fuentes and Vincent Moulton and Katharina T. Huber and Joan Carles Pons},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25177},
eprint = {2609.25177},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25177},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Characterization of tree-child networks in terms of mu vectors
AU - Toni Fuentes
AU - Vincent Moulton
AU - Katharina T. Huber
AU - Joan Carles Pons
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25177
UR - https://arxiv.org/abs/2609.25177
AB - 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.
ER -