English

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 K4K_4 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 22-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}
}