Embedding 4-Chromatic Graphs in the Plane

In Chaps. 1 and 2 , we got acquainted with examples of 4-chromatic unit distance graphs, the Mosers spindle, and the Golomb graph. In Chaps. 5 and 12 , we encountered Paul Erdős’ $25 Problem 5.6 and its partial solution by Nicholas Wormald, who used Blanche Descartes’ construction of a 4-chromatic graph and his own embedding of that graph in the plane. Wormald’s result was improved time and again on the pages of Geombinatorics by Paul O’Donnell, Rob Hochberg, and Kiran Chilacamari. Upon constructing a promising graph G, the authors of the new 4-chromatic unit distance examples used a two-part approach to complete their task: