A Short Note on the Exact Counting of Tree-Child Networks
Michael Fuchs, Hexuan Liu, Guan-Ru Yu

TL;DR
This paper proves a conjecture relating tree-child networks to specific words, focusing on the class of one-component networks, which are significant in phylogenetics for modeling complex evolutionary histories.
Contribution
It establishes the conjecture for one-component tree-child networks, advancing understanding of their combinatorial structure in phylogenetics.
Findings
Proved the conjecture for one-component tree-child networks.
Enhanced understanding of the combinatorial properties of these networks.
Contributed to the mathematical foundation of phylogenetic network modeling.
Abstract
Tree-child networks are an important network class which are used in phylogenetics to model reticulate evolution. In a recent paper, Pons and Batle (2021) conjectured a relation between tree-child networks and certain words. In this short note, we prove their conjecture for the (important) class of one-component tree-child networks.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Advanced Graph Theory Research
