Graph minimization, focusing on the example of 5-chromatic unit-distance graphs in the plane

Abstract

We introduce a new graph minimization method, in which it is required to preserve some graph property and there is an effective procedure for checking this property. We applied this method to minimize 5-chromatic unit-distance graphs and obtained a graph with 509 vertices and 2442 edges.

Fixed typos in matrices. Some changes in references

Cited by in corpus (3)

• All finite sets are Ramsey in the maximum norm
• The chromatic number of the plane is at least 5 -- a human-verifiable proof
• What percent of the plane can be properly 5- and 6-colored?