A proof of the four-colour theorem
A proof of the four-colour theorem
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.
four colour theorem, hand-checkable proof, graph theory
University of Southampton
Xing, Jing Tang
d4fe7ae0-2668-422a-8d89-9e66527835ce
18 September 2013
Xing, Jing Tang
d4fe7ae0-2668-422a-8d89-9e66527835ce
Xing, Jing Tang
(2013)
A proof of the four-colour theorem
Southampton, GB.
University of Southampton
13pp.
Record type:
Monograph
(Discussion Paper)
Abstract
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.
Text
4colourtheoremJTX2013.pdf
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More information
Published date: 18 September 2013
Keywords:
four colour theorem, hand-checkable proof, graph theory
Organisations:
Fluid Structure Interactions Group
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Local EPrints ID: 356984
URI: http://eprints.soton.ac.uk/id/eprint/356984
PURE UUID: 514d4e71-2980-47d1-8bcc-cfca38e4db3f
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Date deposited: 14 Oct 2013 10:58
Last modified: 14 Mar 2024 14:54
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