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Graphs and Combinatorics

, Volume 30, Issue 1, pp 71–81 | Cite as

On the Chromatic Number of Subsets of the Euclidean Plane

  • M. AxenovichEmail author
  • J. Choi
  • M. Lastrina
  • T. McKay
  • J. Smith
  • B. Stanton
Original Paper

Abstract

The chromatic number of a subset of the real plane is the smallest number of colors assigned to the elements of that set such that no two points at distance 1 receive the same color. It is known that the chromatic number of the plane is at least 4 and at most 7. In this note, we determine the bounds on the chromatic number for several classes of subsets of the plane such as extensions of the rational plane, sets in convex position, infinite strips, and parallel lines.

Keywords

Chromatic number of the plane Unit distance graph Coloring the plane 

Mathematics Subject Classification (1991)

Primary 05C12 05C15 05C62 51K99 

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Copyright information

© Springer Japan 2012

Authors and Affiliations

  • M. Axenovich
    • 1
    Email author
  • J. Choi
    • 1
  • M. Lastrina
    • 1
  • T. McKay
    • 1
  • J. Smith
    • 1
  • B. Stanton
    • 1
  1. 1.Department of MathematicsIowa State UniversityAmesUSA

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