Asymmetric 2-colorings of planar graphs in $S^2$ and $S^3$
Erica Flapan, Sarah Crown Rundell, Madeline K. Wyse · arXiv (Cornell University) · 2012
We show that the edges of every 3-connected planar graph except $K_4$ can be colored with two colors so that every embedding of the graph in $S^3$ is asymmetric, and we characterize all planar graphs whose edges can be 2-colored so that every embedding of the graph in $S^2$ is asymmetric.