Encoding and ordering X-cactuses
Andrew Francis, Katharina T. Huber, Vincent Moulton, Taoyang, Wu

TL;DR
This paper introduces a novel encoding for X-cactuses, a type of phylogenetic network, and explores their structural properties and partial orderings to advance phylogenetic network analysis.
Contribution
It presents a new encoding method for X-cactuses using partitions of species set X and defines a partial order on these structures, extending phylogenetic tree properties.
Findings
Developed an encoding of X-cactuses via partitions of X
Defined a partial order on X-cactuses and analyzed its properties
Extended fundamental properties of phylogenetic trees to X-cactuses
Abstract
Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are commonly used to represent the evolution of species which cross with one another. A special type of phylogenetic network is an {\em -cactus}, which is essentially a cactus graph in which all vertices with degree less than three are labelled by at least one element from a set of species. In this paper, we present a way to {\em encode} -cactuses in terms of certain collections of partitions of that naturally arise from -cactuses. Using this encoding, we also introduce a partial order on the set of -cactuses (up to isomorphism), and derive some structural properties of the resulting partially ordered set. This includes an analysis of some properties of its least upper and greatest lower bounds. Our results not only extend some fundamental properties of phylogenetic trees to…
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Taxonomy
TopicsGenomics and Phylogenetic Studies · Plant Diversity and Evolution
