Region colorings for spatial graphs (Women in Mathematics)

Abstract

A Dehn p-coloring for a spatial graph diagram is an assignment of an element (color) of Zp={1, 2, ··· , P-1} to each region of the diagram. At each crossing, some coloring condition is satisfied. We give a family of spatial graph invariants and classify the vertex conditions of Dehn colorings. Some examples of spatial graphs can be distinguished by the number of Dehn colorings by selecting an appropriate vertex condition, whereas they cannot be distinguished by the number of Dehn colorings with no vertex condition. This is joint work with Kanako Oshiro (Sophia University).