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Hyperbolic Tessellation and Colorings of Trees

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  • Dong Han Kim
  • Seonhee Lim

Abstract

We study colorings of a tree induced from isometries of the hyperbolic plane given an ideal tessellation. We show that, for a given tessellation of the hyperbolic plane by ideal polygons, a coloring can be associated with any element of Isom( ), and the element is a commensurator of if and only if its associated coloring is periodic, generalizing a result of Hedlund and Morse.

Suggested Citation

  • Dong Han Kim & Seonhee Lim, 2013. "Hyperbolic Tessellation and Colorings of Trees," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, June.
    • Handle: RePEc:hin:jnlaaa:706496
    DOI: 10.1155/2013/706496
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