Physical Sciences and Mathematics Commons^™

Asymmetric Two-Colourings Of Graphs In S³, Erica Flapan, David Linnan Li

Pomona Faculty Publications and Research

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 K_3,3 or K₅, then G is intrinsically asymmetric. No such asymmetric two-colouring is possible for K_3,3 or K₅.