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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An unavoidable set of $ D$-reducible configurations


Author: John P. Steinberger
Journal: Trans. Amer. Math. Soc. 362 (2010), 6633-6661
MSC (2000): Primary 05C15
Published electronically: July 9, 2010
MathSciNet review: 2678989
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Abstract: We give a new proof of the four-color theorem by exhibiting an unavoidable set of 2822 $ D$-reducible configurations. The existence of such a set had been conjectured by several researchers including Stromquist (1975), Appel and Haken (1977), and Robertson, Sanders, Seymour and Thomas (1997).


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Additional Information

John P. Steinberger
Affiliation: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada V6T 1Z2
Address at time of publication: Department of Mathematics, FIT Building 1-208, Tsinghua University, Beijing, 100084, People’s Republic of China
Email: jpsteinb@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05092-5
PII: S 0002-9947(2010)05092-5
Keywords: Graph theory, four-color theorem
Received by editor(s): July 7, 2008
Received by editor(s) in revised form: April 23, 2009
Published electronically: July 9, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.