Enumerative combinatorics of unlabeled and labeled time-consistent galled trees

2025/04/22 by Agranat-Tamir, Lily, Fuchs, Michael, Gittenberger, Bernhard +1 · 1 citation
#Combinatorics (math.CO) #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE)

paper · doi:10.48550/arxiv.2504.16302

Abstract

In mathematical phylogenetics, the time-consistent galled trees provide a simple class of rooted binary network structures that can be used to represent a variety of different biological phenomena. We study the enumerative combinatorics of unlabeled and labeled time-consistent galled trees. We present a new derivation via the symbolic method of the number of unlabeled time-consistent galled trees with a fixed number of leaves and a fixed number of galls. We also derive new generating functions and asymptotics for labeled time-consistent galled trees.

Citations

• Asymptotic enumeration of normal and hybridization networks via tree decoration
• Sackin Indices for Labeled and Unlabeled Classes of Galled Trees
• Galled Tree-Child Networks
• Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks
• Classes of Explicit Phylogenetic Networks and their Biological and Mathematical Significance
• Counting Phylogenetic Networks with Few Reticulation Vertices: A Second Approach
• Counting and enumerating tree-child networks and their subclasses
• Asymptotic Enumeration and Distributional Properties of Galled Networks
• Counting Phylogenetic Networks with Few Reticulation Vertices: Exact Enumeration and Corrections
• Counting General Phylogenetic networks
• On the Asymptotic Growth of the Number of Tree-Child Networks
• Counting Phylogenetic Networks of level 1 and 2
• Generating Normal Networks via Leaf Insertion and Nearest Neighbor Interchange
• Counting and Enumerating Galled Networks
• Counting Phylogenetic Networks with Few Reticulation Vertices: Tree-Child and Normal Networks
• The Number of Evolutionary Trees

Cited by

• A dichotomy law for certain classes of phylogenetic networks

Related

• Counting and Enumerating Galled Networks
• Asymptotic Enumeration and Distributional Properties of Galled Networks
• Counting Tree-Child Networks and Their Subclasses
• Counting Phylogenetic Networks of level 1 and 2
• Structure and Recognition of 3,4-leaf Powers of Galled Phylogenetic Networks in Polynomial Time