Flowers in graph-like spaces
Combinatorics
2023-12-22 v1
Abstract
One perspective on tree decompositions is that they display (low-order) separations of the underlying graph or matroid. The separations displayed by a tree decomposition are necessarily nested. In 2013, Clark and Whittle proved the existence of tree decompositions with flowers added in which, up to a natural equivalence, all low-order separations are displayed. An important step in that proof is to show that flowers can be extended to maximal flowers. In this paper we generalise the notion of a flower to pseudoflowers in graph-like spaces and show for our generalisation, flowers can be extended to maximal flowers.
Keywords
Cite
@article{arxiv.2312.13825,
title = {Flowers in graph-like spaces},
author = {Ann-Kathrin Elm and Hendrik Heine},
journal= {arXiv preprint arXiv:2312.13825},
year = {2023}
}
Comments
37 pages, including 7 pages of appendix, and 11 figures