Abstract by Matthew Hague
A variation on the Hadwiger-Nelson graph coloring problem
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.