A New Proof of the Four-Colour Theorem

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A new proof of the four-colour theorem

Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas

Abstract.

The four-colour theorem, that every loopless planar graph admits a vertex-colouring with at most four different colours, was proved in 1976 by Appel and Haken, using a computer. Here we announce another proof, still using a computer, but simpler than Appel and Haken's in several respects.

Copyright N. Robertson, D. P. Sanders, P. Seymour, R. Thomas 1996

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Article Info

ERA Amer. Math. Soc. 02 (1996), pp. 17-25
Publisher Identifier: S 1079-6762(96)00003-5
1991 Mathematics Subject Classification. Primary 05C10, 05C15, 05C85
Received by the editors September 26, 1995
Communicated by Ronald Graham
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Neil Robertson

Department of Mathematics, Ohio State University, 231 W. 18th Ave., Columbus, Ohio 43210, USA

E-mail address: robertso@math.ohio-state.edu

Daniel P. Sanders

School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

E-mail address: dsanders@math.ohio-state.edu

Paul Seymour

Bellcore, 445 South Street, Morristown, New Jersey 07960, USA

E-mail address: pds@bellcore.com

Robin Thomas

School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

E-mail address: thomas@math.gatech.edu

Research partially performed under a consulting agreement with Bellcore, and partially supported by DIMACS Center, Rutgers University, New Brunswick, New Jersey 08903, USA.
Neil Robertson was partially supported by NSF under Grant No. DMS-8903132 and by ONR under Grant No. N00014-92-J-1965.
Daniel P. Sanders was partially supported by DIMACS and by ONR under Grant No. N00014-93-1-0325.
Robin Thomas was partially supported by NSF under Grant No. DNS-9303761 and by ONR under Grant No. N00014-93-1-0325.

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