Canonical decompositions and algorithmic recognition of spatial graphs

Stefan Friedl; Lars Munser; José Pedro Quintanilha; Yuri Santos Rego

doi:10.1017/s0013091524000087

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arXiv · 2105.06905

Canonical decompositions and algorithmic recognition of spatial graphs

Stefan Friedl·Lars Munser·José Pedro Quintanilha·Yuri Santos Rego

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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.

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Stefan Friedl, Lars Munser, José Pedro Quintanilha, Yuri Santos Rego. 2021-05-14. Canonical decompositions and algorithmic recognition of spatial graphs. https://doi.org/10.1017/s0013091524000087

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