Orientability of Phylogenetic Network Graphs

Traditionally, genetic history of species has been modeled using phylogenetic trees. Recently, scientists have begun using phyolgenetic networks to model more complex occurrences, such as hybridization, which cannot be displayed by trees. Phylogenetic networks are represented by network graphs which are trivalent, directed graphs without directed circuits. In this paper we discuss the mathematics of network graphs. Given an unoriented trivalent graph, we determine a necessary and sufficient condition for orienting the graph as a network graph

A concise necessary and sufficient condition for the existence of a galled-tree

Abstract — Galled-trees are a special class of graphical representation of evolutionary history that has proved amenable to efficient, polynomial-time algorithms. The goal of this paper is to construct a concise necessary and sufficient condition for the existence of a galled-tree for M, a set of binary sequences that purportedly have evolved in the presence of recombination. Both root-known and rootunknown cases are considered here. Index Terms—Galled-trees, recombination, quadpartition, incompatibility