Asymmetric $2$-colorings of graphs
Combinatorics
2016-08-26 v4 Geometric Topology
Abstract
We show that the edges of every 3-connected planar graph except can be colored with two colors in such a way that the graph has no color preserving automorphisms. Also, we characterize all graphs which have the property that their edges can be -colored so that no matter how the graph is embedded in any orientable surface, there is no homeomorphism of the surface which induces a non-trivial color preserving automorphism of the graph.
Keywords
Cite
@article{arxiv.1206.1945,
title = {Asymmetric $2$-colorings of graphs},
author = {Erica Flapan and Sarah Rundell and Madeline Wyse},
journal= {arXiv preprint arXiv:1206.1945},
year = {2016}
}