Carsten Thomassen’s 7-Color Theorem

One day in 1998, I was asked by The American Mathematical Monthly to referee a manuscript submitted by one of the world’s leading graph theorists, Professor Carsten Thomassen of the Technical University of Denmark. The paper offered a fresh, purely graph-theoretic approach to finding the chromatic number of the plane. I was very impressed, asked the author to expand his too concise (for The Monthly) presentation, and informed him of my research that proved that Edward Nelson, and Nelson alone (without Hadwiger), was the author of the problem. Of course, I recommended Monthly to publish this work. In this chapter, I will present Thomassen’s attempt to find the chromatic number of the plane. He has not found it – no one has – but he obtained a fine result and, in the process, showed how graph theory proper can be utilized in an assault on this problem. I will present Thomassen’s proof with minor editorial revisions. The use of paper and pencil is a must while reading the proof written in Thomassen’s style.