Graphical Neighborhoods of Spatial Graphs

Friedl, Stefan; Herrmann, Gerrit

doi:10.1007/978-3-030-62497-2_38

Cited by 3 publications

(2 citation statements)

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“…We have decided to work in the PL setting because it is the natural home for results in computational topology such as our main theorem, and it is the framework of the machinery developed by Matveev on which we rely. This is a standard framework in the field [Suz70; Kau89; Yam89; Bar15], although a theory of smooth, rather than PL, spatial graphs has also been introduced by Herrmann and the first author [FH20;FH21].…”

Section: The Piecewise-linear Settingmentioning

confidence: 99%

Canonical decompositions and algorithmic recognition of spatial graphs

Friedl,

Munser,

Quintanilha

et al. 2021

Preprint

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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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Section: The Piecewise-linear Settingmentioning

confidence: 99%

Canonical decompositions and algorithmic recognition of spatial graphs

Friedl,

Munser,

Quintanilha

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The PL category is the natural home for results in computational topology, such as our main theorem and the machinery in Matveev’s text. It is a standard framework in the field [3, 10, 16, 17], although a theory of smooth, rather than PL, spatial graphs has also been introduced by the first author and Herrmann [4, 5].…”

Section: Introductionmentioning

confidence: 99%

Canonical decompositions and algorithmic recognition of spatial graphs

Friedl,

Munser,

Quintanilha

et al. 2024

Proceedings of the Edinburgh Mathematical Society

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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.

show abstract