non-planar graph, intrinsic chirality, 3-connected graph
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.
© 2002 Cambridge Philosophical Society
ERICA FLAPAN and DAVID LINNAN LI (2002). Asymmetric two-colourings of graphs in S3. Mathematical Proceedings of the Cambridge Philosophical Society, 132, pp 267-280. doi:10.1017/S0305004101005643.