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Canonical decompositions and algorithmic recognition of spatial graphs
Published online by Cambridge University Press: 14 March 2024
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.
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society