De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating
that the solution to the Hadwiger-Nelson problem
(i.e., the chromatic number of the plane) is at least 5. While de Grey's original
vertices, he was able to reduce this number (after a correction) to the 1581-vertex
graph illustrated above (de Grey 2018), referred to in this work as the de Grey graph.
A few days after the original preprint was published, Mixon (2018) constructed a similar 1585-vertex graph, the removal of 8 vertices from which led to an even smaller
1577-vertex graph. This work terms these two graphs the Mixon