Embedding 4-Chromatic Graphs in the Plane

Alexander Soifer
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Alexander Soifer: University of Colorado at Colorado Springs, College of Letters, Arts, and Sciences

Chapter Chapter 14 in The New Mathematical Coloring Book, 2024, pp 117-126 from Springer

Abstract: Abstract 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:

Date: 2024
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DOI: 10.1007/978-1-0716-3597-1_14

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