BYU

Abstract by Matthew Hague

Personal Infomation


Presenter's Name

Matthew Hague

Degree Level

Undergraduate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Curtis Kent

Title

A variation on the Hadwiger-Nelson graph coloring problem

Abstract

In graph theory, the Hadwiger–Nelson problem, asks for the minimum number of colors required to color the plane such that no two points, that are distance 1 apart, have the same color. We ask a similar question about stable colorings of the plane. Under the L1-norm and the L(infinity)-norm, we know that the plane can be colored, in a way that remains valid after small perturbations in the metric, with 4 colors. In the L2-norm, it has been shown that this minimal coloring uses at least 5 colors and a maximum of 7. Using computational methods, we hope to show that stable colorings of the plane in the L2-norm require at least 7 colors, or find interesting results concerning the properties of theoretical 6 colorings.