Uniquely Pressable Graphs: Characterization, Enumeration, and Recognition
Combinatorics
2017-06-26 v1
Abstract
We consider "pressing sequences", a certain kind of transformation of graphs with loops into empty graphs, motivated by an application in phylogenetics. In particular, we address the question of when a graph has precisely one such pressing sequence, thus answering an question from Cooper and Davis (2015). We characterize uniquely pressable graphs, count the number of them on a given number of vertices, and provide a polynomial time recognition algorithm. We conclude with a few open questions. Keywords: Pressing sequence, adjacency matrix, Cholesky factorization, binary matrix
Keywords
Cite
@article{arxiv.1706.07468,
title = {Uniquely Pressable Graphs: Characterization, Enumeration, and Recognition},
author = {Joshua N. Cooper and Hays W. Whitlatch},
journal= {arXiv preprint arXiv:1706.07468},
year = {2017}
}
Comments
30 pages. Keywords: Pressing sequence, adjacency matrix, Cholesky factorization, binary matrix