Asymmetric two-colourings of graphs in S3
Erica Flapan, David Linnan Li · Mathematical Proceedings of the Cambridge Philosophical Society · 2002
We prove that for any non-planar graph H, we can choose a two-colouring G of H such that G is intrinsically chiral, and if H is 3-connected and is not K3,3 or K5, then G is intrinsically asymmetric. No such asymmetric two-colouring is possible for K3,3 or K5.