A Proof of the Four Colour Theorem
Jing Tang Xing · ePrints Soton (University of Southampton) · 2013
The four-colour problem remained unsolved for more than a hundred years has played a role of the utmost importance in the development of graph theory. The four-colour theorem was confirmed in 1976, which is not completely satisfied due to: i) part of the proof using computers cannot be verified by hand; ii) even the part, supposedly hand-checkable, is extraordinarily complicated and tedious, and as far as we know, no one has entirely verified it. Seeking a hand-checkable proof of the four-colour theorem is one of world-interested problems, which is addressed in this paper. A necessary and sufficient condition for n-colour theorem in a space is: there exists a largest n-complete graph base in the same space. Examples are given to illustrate applications.