空间图的典型分解和算法识别

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-03-14 DOI:10.1017/s0013091524000087

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

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引用次数: 0

摘要

我们证明存在一种算法，可以确定两个片状线性空间图是否同构。我们首先证明了空间图在适当的拓扑学意义上可以被典型地分解为块，即非分裂且没有切割顶点的空间图。然后，我们应用哈肯和马特维耶夫的一个结果，以算法区分这些块。

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Canonical decompositions and algorithmic recognition of spatial graphs

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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来源期刊

Proceedings of the Edinburgh Mathematical Society 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.