When can splits be drawn in the plane?
Populations and Evolution
2015-09-22 v1 Combinatorics
Abstract
Split networks are a popular tool for the analysis and visualization of complex evolutionary histories. Every collection of splits (bipartitions) of a finite set can be represented by a split network. Here we characterize which collection of splits can be represented using a planar split network. Our main theorem links these collections of splits with oriented matroids and arrangements of lines separating points in the plane. As a consequence of our main theorem, we establish a particularly simple characterization of maximal collections of these splits.
Cite
@article{arxiv.1509.06104,
title = {When can splits be drawn in the plane?},
author = {Monika Balvočiūtė and David Bryant and Andreas Spillner},
journal= {arXiv preprint arXiv:1509.06104},
year = {2015}
}