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math.CO2026

Note on the Maximum Number of Trees Displayed by a Tree-Child Network

Yukihiro Murakami, Charles Semple

In this note, we show that, for all , the number of distinct rooted binary phylogenetic -trees displayed by a binary tree-child network on with lea…

math.CO2025

Binary normal networks without near reticulations can be reconstructed from their rooted triples

Andrew Francis, Charles Semple

Normal networks are an important class of phylogenetic networks that have compelling mathematical properties which align with intuition about inference from genetic data. While too…

math.CO2025

Bounding the SNPR distance between two tree-child networks using generalised agreement forests

Steven Kelk, Simone Linz, Charles Semple

Agreement forests continue to play a central role in the comparison of phylogenetic trees since their introduction more than 25 years ago. More specifically, they are used to chara…

math.CO2025

A sharp lower bound for the number of phylogenetic trees displayed by a tree-child network

Charles Semple, Kristina Wicke

A normal (phylogenetic) network with reticulations displays phylogenetic trees. In this paper, we establish an analogous result for tree-child (phylogenetic) networks wit…

math.CO2024

When is a set of phylogenetic trees displayed by a normal network?

Magnus Bordewich, Simone Linz, Charles Semple

A normal network is uniquely determined by the set of phylogenetic trees that it displays. Given a set of rooted binary phylogenetic trees, this paper presents a poly…