Palettes of Dehn colorings for spatial graphs and the classification of vertex conditions.

In this paper, we study Dehn colorings of spatial graph diagrams, and classify the vertex conditions, equivalently the palettes, for them. We give some example of spatial graphs that 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.