Discrete Approximation of Coloring the Plane

  • Angel Chavez California State University, Los Angeles
  • Gwen Ostergren California State University, Los Angeles
Keywords: graph coloring; coloring the plane

Abstract

 This work is inspired by the open problem The Chromatic Number of The Plane. We approximate the plane by only considering points with coordinates (p/n, q/n), where p and q are integers, and n is a fixed positive integer. To prevent triviality, we add the restriction that two points are adjacent if and only if their distance is between 1-ε and 1+ε for a non-negative ε. Adjacent points have to be colored differently. Our goal is to find the smallest ε for each n that will force us to use five colors.

Published
2019-02-08
How to Cite
Chavez, A., & Ostergren, G. (2019). Discrete Approximation of Coloring the Plane. The PUMP Journal of Undergraduate Research, 2, 20-29. Retrieved from https://journals.calstate.edu/pump/article/view/227