Properties of the Unit Distance Graph of the Plane

Properties of the Unit Distance Graph of the Plane

Explore the properties of the unit distance graph of the plane in this hour-long conference talk by Máté Matolcsi at ICBS2024. Delve into the famous Hadwiger-Nelson problem, which seeks to determine the chromatic number of the unit distance graph UDG(ℝ²) of the plane. Discover the minimal number of colors needed to color the plane such that any pair of points at distance 1 have different colors. Examine related problems on various parameters of the unit distance graph, including a proof of Erdos' conjecture that any measurable subset of ℝ² avoiding the unit distance must have an upper density of