Slim Sets of Binary Trees
Stefan Gr\"unewald

TL;DR
This paper investigates compatibility conditions for sets of binary phylogenetic trees, providing a sufficient condition for compatibility and a new proof for the minimal cardinality characterization of quartet sets that are uniquely displayed by a single phylogenetic tree.
Contribution
It introduces a new sufficient condition for compatibility of binary phylogenetic trees and offers a concise proof for the minimal cardinality characterization of uniquely displayed quartet sets.
Findings
Proves a new sufficient condition for compatibility of binary phylogenetic trees.
Provides a short, self-contained proof for the minimal cardinality characterization of quartet sets.
Enhances understanding of compatibility and uniqueness in phylogenetic tree sets.
Abstract
A classical problem in phylogenetic tree analysis is to decide whether there is a phylogenetic tree that contains all information of a given collection of phylogenetic trees. If the answer is "yes" we say that is compatible and displays . This decision problem is NP-complete even if all input trees are quartets, that is binary trees with exactly four leaves. In this paper, we prove a sufficient condition for a set of binary phylogenetic trees to be compatible. That result is used to give a short and self-contained proof of the known characterization of quartet sets of minimal cardinality which are displayed by a unique phylogenetic tree.
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Taxonomy
TopicsGenomics and Phylogenetic Studies
