Exploring 6- or 7-Chromatic Unit Distance Graphs in the Plane

The concept of unit distance graphs is fundamental in geometric graph theory, where vertices are points in the Euclidean plane and edges connect pairs of vertices exactly one unit apart. A major open problem in this area is determining the chromatic number of such graphs — the minimum number of colors needed to color the vertices so that no two adjacent vertices share the same color. In this talk, I will explore the construction and analysis of unit distance graphs that require 5, 6, or possibly 7 colors for proper coloring, using an approach based on the angular orientation of the Moser Spindle and translation techniques.