Classes of treebased networks

TL;DR

This paper investigates classes of treebased phylogenetic networks, providing criteria for their identification, exploring their relation to generalized series parallel graphs, and introducing new classes with analyzed relationships.

Contribution

It introduces linear-time verifiable criteria for treebasedness and explores the relationship between edgebased networks and generalized series parallel graphs.

Findings

Edgebased networks are related to generalized series parallel graphs.

Linear-time verification of edgebasedness is possible.

New classes of treebased networks are introduced and analyzed.

Abstract

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 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 edgebasedness, can be verified in linear time. Surprisingly, the class of edgebased networks is closely related to a well-known family of graphs, namely the class of generalized series parallel graphs, and we will explore this relationship in full detail. Additionally, we introduce further classes of treebased networks and analyze their relationships.