Classes of treebased networks.

Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the \emph{base tree}, by adding additional edges. The main aim of this manuscript is to provide some sufficient criteria for treebasedness by reducing phylogenetic networks to related graph structures. While it is generally known that deciding whether a network is treebased is NP-complete, one of these criteria, namely \emph{edgebasedness}, can be verified in polynomial time. Next to these edgebased networks, we introduce further classes of treebased networks and analyze their relationships.