In this paper, we study Dehn colorings of spatial graph diagrams, and classify the vertex conditions, equivalently the palettes. We give some example of spatial graphs which can be distinguished by the number of Dehn colorings with selecting an appropriate palette. Furthermore, we also discuss the generalized version of palettes, which is defined for knot-theoretic ternary-quasigroups and region colorings of spatial graph diagrams.

中文翻译：

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用于空间图和顶点条件分类的 Dehn 着色调色板

在本文中，我们研究了空间图的德恩着色，并对顶点条件进行了分类，相当于调色板. 我们给出了一些空间图的例子，可以通过选择适当的调色板来区分 Dehn 着色的数量。此外，我们还讨论了调色板的广义版本，它是为节点理论三元拟群和空间图的区域着色定义的。