Rooted phylogenetic networks are rooted acyclic digraphs. They are used to model complex evolution where hybridization, recombination, and other reticulation events play a role. A rigorous definition of network compression is introduced on the basis of recent studies of relationships between cluster, tree, and rooted phylogenetic networks. The concept reveals new connections between well-studied network classes, including tree–child networks and reticulation-visible networks. It also enables us to define a new class of networks for which the cluster containment problem is solvable in linear time.
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