Canonical decompositions and algorithmic recognition of spatial graphs
Geometric Topology
2024-05-22 v1
Abstract
We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colorings, edge colorings and/or edge orientations. We first show that spatial graphs admit canonical decompositions into blocks, that is, spatial graphs that are non-separable and have no cut vertices, in a suitable topological sense. Then we apply a result of Haken and Matveev in order to algorithmically distinguish these blocks.
Keywords
Cite
@article{arxiv.2105.06905,
title = {Canonical decompositions and algorithmic recognition of spatial graphs},
author = {Stefan Friedl and Lars Munser and José Pedro Quintanilha and Yuri Santos Rego},
journal= {arXiv preprint arXiv:2105.06905},
year = {2024}
}
Comments
57 pages, 16 figures