Classes of tree-based networks

• Main Authors: Mareike Fischer, Michelle Galla, Lina Herbst, Yangjing Long, Kristina Wicke
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Visual Computing for Industry, Biomedicine, and Art
• Subjects: Phylogenetic tree; Phylogenetic network; Tree-based network; Edge-based network; Chordal network; Hamilton connected
• Online Access: http://link.springer.com/article/10.1186/s42492-020-00043-z

Abstract Recently, so-called tree-based phylogenetic networks have attracted considerable attention. These networks can be constructed from a phylogenetic tree, called the base tree, by adding additional edges. The primary aim of this study is to provide sufficient criteria for tree-basedness by reducing phylogenetic networks to related graph structures. Even though it is generally known that determining whether a network is tree-based is an NP-complete problem, one of these criteria, namely edge-basedness, can be verified in linear time. Surprisingly, the class of edge-based networks is closely related to a well-known family of graphs, namely, the class of generalized series-parallel graphs, and we explore this relationship in full detail. Additionally, we introduce further classes of tree-based networks and analyze their relationships.