ABSTRACT
Since 1890 a great many attempts have been made to find a proof of the Four Color Theorem. This chapter distinguishes two types of such attempts: attempts to repair the flaw in A. B. Kempe’s work; and attempts to find new and different approaches to the problem. In H. Heesch treats several special cases of triangulations and proves that each of them contains a reducible configuration. The cooperation between Heesch and Haken was interrupted in October 1971 when the work of Shimamoto was thought to have settled the Four Color Problem. In 1974, the authors could prove the existence of a finite unavoidable set of geographically good configurations and describe an algorithm for constructing such a set. By September 1975 the authors had improved the methods so far that it seemed to be more work to change the computer program after each new improvement than to carry out the case enumeration by hand.
