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Phylogenetic networks are used to study evolutionary relationships betweenspecies in biology. Such networks are often categorized into classes by theirtopological features, which stem from both biological and computationalmotivations. We study two network classes in this paper: tree-based networksand orchard networks. Tree-based networks are those that can be obtained byinserting edges between the edges of an underlying tree. Orchard networks are arecently introduced generalization of the class of tree-child networks.Structural characterizations have already been discovered for tree-basednetworks; this is not the case for orchard networks. In this paper, weintroduce cherry covers---a unifying characterization of both networkclasses---in which we decompose the edges of the networks into so-called cherryshapes and reticulated cherry shapes. We show that cherry covers can be used tocharacterize the class of tree-based networks as well as the class of orchardnetworks. Moreover, we also generalize these results to non-binary networks.

A Unifying Characterization of Tree-based Networks and Orchard Networks using Cherry Covers