When Can Splits be Drawn in the Plane?
Pages 839 - 856
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.
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DOI:10.1137/sjdmec.31.2
Issue’s Table of Contents© 2017, Society for Industrial and Applied Mathematics.
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Society for Industrial and Applied Mathematics
United States
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Published: 01 January 2017
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