Print Email Facebook Twitter A unifying characterization of tree-based networks and orchard networks using cherry covers Title A unifying characterization of tree-based networks and orchard networks using cherry covers Author van Iersel, L.J.J. (TU Delft Discrete Mathematics and Optimization) Janssen, R. (TU Delft Discrete Mathematics and Optimization) Jones, M.E.L. (TU Delft Discrete Mathematics and Optimization; Centrum Wiskunde & Informatica (CWI)) Murakami, Yukihiro (TU Delft Discrete Mathematics and Optimization) Zeh, Norbert (Dalhousie University) Date 2021 Abstract Phylogenetic networks are used to represent evolutionary relationships between species in biology. Such networks are often categorized into classes by their topological features, which stem from both biological and computational motivations. We study two network classes in this paper: tree-based networks and orchard networks. Tree-based networks are those that can be obtained by inserting edges between the edges of an underlying tree. Orchard networks are a recently introduced generalization of the class of tree-child networks. Structural characterizations have already been discovered for tree-based networks; this is not the case for orchard networks. In this paper, we introduce cherry covers—a unifying characterization of both network classes—in which we decompose the edges of the networks into so-called cherry shapes and reticulated cherry shapes. We show that cherry covers can be used to characterize the class of tree-based networks as well as the class of orchard networks. Moreover, we also generalize these results to non-binary networks. Subject Graph theoryPhylogenetic networksPhylogenetics To reference this document use: http://resolver.tudelft.nl/uuid:e3307580-bd67-448d-97ba-29938c50e07a DOI https://doi.org/10.1016/j.aam.2021.102222 ISSN 0196-8858 Source Advances in Applied Mathematics, 129, 1-23 Part of collection Institutional Repository Document type journal article Rights © 2021 L.J.J. van Iersel, R. Janssen, M.E.L. Jones, Yukihiro Murakami, Norbert Zeh Files PDF 1_s2.0_S0196885821000609_main.pdf 555.24 KB Close viewer /islandora/object/uuid:e3307580-bd67-448d-97ba-29938c50e07a/datastream/OBJ/view