# Generation of Tree-Child phylogenetic networks

## TL;DR

This paper introduces an efficient recursive method for generating all binary tree-child phylogenetic networks with a specified number of leaves, extending known operations for phylogenetic trees and providing bounds on their quantity.

## Contribution

It presents a novel recursive algorithm for generating binary tree-child networks and generalizes reduction/augmentation operations from phylogenetic trees.

## Key findings

- Provides a recurrence relation for counting networks
- Offers an efficient generation algorithm
- Extends operations from phylogenetic trees

## Abstract

Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary tree-child networks is one of the most studied ones. However, very little is known about the combinatorial structure of these networks. In this paper we address the problem of generating all possible binary tree-child networks with a given number of leaves in an efficient way via reduction/augmentation operations that extend and generalize analogous operations for phylogenetic trees and are biologically relevant. Since our solution is recursive, this also provides us with a recurrence relation giving an upper bound on the number of such networks.