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.

中文翻译：

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空间图的规范分解和算法识别

我们证明存在一种算法可以确定两个分段线性空间图是否同构。在最一般的形式中，我们的定理适用于具有顶点着色、边缘着色和/或边缘方向的空间图。我们首先证明空间图允许规范分解为块，即在适当的拓扑意义上，空间图是不可分割的并且没有割点。然后，我们应用 Haken 和 Matveev 的结果来通过算法区分这些块。