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arXiv · 1502.07450

Successful Pressing Sequences for a Bicolored Graph and Binary Matrices

Joshua Cooper·Jeffrey Davis
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Abstract

We apply matrix theory over $\mathbb{F}_2$ to understand the nature of so-called "successful pressing sequences" of black-and-white vertex-colored graphs. These sequences arise in computational phylogenetics, where, by a celebrated result of Hannenhalli and Pevzner, the space of sortings-by-reversal of a signed permutation can be described by pressing sequences. In particular, we offer several alternative linear-algebraic and graph-theoretic characterizations of successful pressing sequences, describe the relation between such sequences, and provide bounds on the number of them. We also offer several open problems that arose as a result of the present work.

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Joshua Cooper, Jeffrey Davis. 2015-02-26. Successful Pressing Sequences for a Bicolored Graph and Binary Matrices. https://arxiv.org/abs/1502.07450

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