  Rooted phylogenetic networks are rooted acyclic digraphs. They are used to
model complex evolution where hybridization, recombination and other
reticulation events play important roles. A rigorous definition of network
compression is introduced on the basis of the recent studies of the
relationships between cluster, tree and rooted phylogenetic network. The
concept reveals another interesting connection between the two well-studied
network classes|tree-child networks and reticulation-visible networks|and
enables us to define a new class of networks for which the cluster containment
problem has a linear-time algorithm.
