Friedl, Stefan and Munser, Lars and Quintanilha, Jose Pedro and Rego, Yuri Santos (2024) Canonical decompositions and algorithmic recognition of spatial graphs. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 67 (2). pp. 388-430. ISSN 0013-0915, 1464-3839
Full text not available from this repository. (Request a copy)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 colourings, edge colourings and/or edge orientations.We first show that spatial graphs admit canonical decompositions into blocks, that is, spatial graphs that are non-split 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; spatial graphs; 3-manifolds with boundary pattern; Haken manifolds; piecewise-linear topology |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Stefan Friedl |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Jul 2025 11:39 |
| Last Modified: | 28 Jul 2025 11:39 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63866 |
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