BYU

Abstract by Sheridan Harding

Personal Infomation


Presenter's Name

Sheridan Harding

Co-Presenters

None

Degree Level

Undergraduate

Co-Authors

None

Abstract Infomation


Department

Mathematics

Faculty Advisor

Curtis Kent

Title

Stable Colorings of the Plane With the L^\infty-metric

Abstract

A coloring of the plane is a map that assigns a color to each point of the plane such
that no two points a distance of one apart share the same color. The chromatic number of
the plane is the minimal number of colors needed to color the plane. We expand on this
definition by saying that a coloring is stable if any small perturbation of the coloring is
also a coloring. The stable chromatic number is the minimal number of colors needed to
color the plane with a stable coloring. We examine the properties of chromatically stable
colorings under the L^\infty-metric on the plane, particularly how the chromatic number of the
plane compares to the stable chromatic number.