Asymmetric \(2\)-colorings of graphs

Asymmetric \(2\)-colorings of graphs

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...

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Veröffentlicht in:arXiv.org 2016-08
Hauptverfasser: Flapan, Erica, Rundell, Sarah, Wyse, Madeline
Format: Artikel
Sprache:eng
Schlagworte:
Automorphisms
Color
Graph theory
Graphs
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Zusammenfassung: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.
ISSN:2331-8422