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arXiv · 1206.1945

Asymmetric $2$-colorings of graphs

Erica Flapan·Sarah Rundell·Madeline Wyse
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Abstract

We show that the edges of every 3-connected planar graph except $K_4$ 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 $2$-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.

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Erica Flapan, Sarah Rundell, Madeline Wyse. 2016-08-25. Asymmetric $2$-colorings of graphs. https://arxiv.org/abs/1206.1945

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