# Rooted NNI moves and distance-1 tail moves on tree-based phylogenetic networks

### Abstract

We show that the space of rooted tree-based phylogenetic networks is connected under rooted nearest-neighbour interchange (rNNI) moves and distance-1 tail moves.

Type
Publication
Discrete Applied Mathematics, Volume 294, 15 May 2021, Pages 205-213

Any two tree-based rooted binary phylogenetic networks (with the same number of reticulation nodes and identical degrees at the root) are connected by at most $(4k+8)\cdot\left(|X|+\frac34k\right)+|X|\cdot\lceil\log_2|X|\rceil$ rooted nearest-neighbor interchange (rNNI) moves. As a corollary of the proof we obtain that the diameter is at most a $2k$ additive term larger for distance-1 tail moves.

###### Mathematician

My research interests include Graph Theory, Computational Geometry, and Algorithms