Colorings of the d-regular infinite tree

  • Authors:

  • Shlomo Hoory;Nathan Linial

  • Affiliations:

  • Department of Computer Science, University of Toronto, Toronto, ON, Canada.;Institute of Computer Science, Hebrew University Jerusalem 91904, Israel

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2004

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Abstract

The existence of small d-regular graphs of a prescribed girth g is equivalent to the existence of certain codes in the d-regular infinite tree. We show that in the tree "perfect" codes exist, but those are usually not "graphic". We also give an explicit coloring that is "nearly perfect" as well as "nearly graphic".