In my latest paper, I present experimental evidence on unit-distance graph density which was introduced by Paul Erdős. My approach is based on a novel algorithmic exploration of the rational plane and the generation of a unit-distance graph that surpasses recent theoretical lower bounds. It achieves a scaling exponent larger than 1.17.
The algorithm essentially utilizes a local-breadth search on a bounded and finite set of elements and generates a graph that potentially encompasses the general properties of a unit-distance graph, not affected by restrictions on its generation.
Find the paper here and the repository containing code and experimental results here.
