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==References== {{refbegin|30em}} * {{Citation |last=Allaire |first=Frank |year=1978 |chapter=Another proof of the four colour theorem. I. |title= Proceedings, 7th Manitoba Conference on Numerical Mathematics and Computing, Congr. Numer. |volume = 20 |pages=3–72 | mr=0535003 | publisher=Utilitas Mathematica Publishing, Inc. | location=Winnipeg, Man. | isbn=0-919628-20-6 | editor1=D. McCarthy | editor2=H. C. Williams}} * {{Citation |last1=Appel |first1=Kenneth |author1-link=Kenneth Appel|last2=Haken |first2=Wolfgang|author2-link= Wolfgang Haken |year=1977 |title=Every Planar Map is Four Colorable. I. Discharging |journal=Illinois Journal of Mathematics| volume=21 |pages=429–490| issue=3 | mr=0543792 |doi=10.1215/ijm/1256049011 |doi-access=free }} * {{Citation |last1=Appel |first1=Kenneth |author1-link=Kenneth Appel|last2=Haken |first2=Wolfgang|author2-link= Wolfgang Haken |last3=Koch |first3=John |year=1977 |title=Every Planar Map is Four Colorable. II. Reducibility |journal=Illinois Journal of Mathematics| volume=21 |pages=491–567| mr=0543793 | issue=3 |doi=10.1215/ijm/1256049012 |doi-access=free }} * {{Citation| doi=10.1038/scientificamerican1077-108|last1=Appel |first1=Kenneth |author1-link=Kenneth Appel|last2=Haken |first2=Wolfgang|author2-link= Wolfgang Haken |date=October 1977 |title=Solution of the Four Color Map Problem |periodical=Scientific American|volume=237 |pages=108–121|issue=4 |bibcode=1977SciAm.237d.108A}} * {{Citation |last1=Appel |first1=Kenneth |author1-link=Kenneth Appel |last2=Haken |first2=Wolfgang |author2-link=Wolfgang Haken |year=1989 |title=Every Planar Map is Four-Colorable |publisher=American Mathematical Society |place=Providence, Rhode Island |isbn=0-8218-5103-9 |mr=1025335 |series=Contemporary Mathematics |volume=98 |others=With the collaboration of J. Koch. |doi=10.1090/conm/098 |s2cid=8735627 |url=http://projecteuclid.org/euclid.bams/1183538218 }} * {{citation | last = Bar-Natan | first = Dror | author-link = Dror Bar-Natan | arxiv = q-alg/9606016 | doi = 10.1007/BF01196130 | issue = 1 | journal = Combinatorica | mr = 1466574 | pages = 43–52 | title = Lie algebras and the four color theorem | volume = 17 | year = 1997| s2cid = 2103049 }} * {{Citation |last=Bernhart|first=Frank R.|year=1977|title= A digest of the four color theorem|periodical= Journal of Graph Theory|volume=1|pages=207–225|doi= 10.1002/jgt.3190010305| issue=3 | mr=0465921}} * {{citation |last = Borodin |first = O. V. |issue = 41 |journal = Metody Diskretnogo Analiza |mr = 832128 |pages = 12–26, 108 |title = Solution of the Ringel problem on vertex-face coloring of planar graphs and coloring of 1-planar graphs |year = 1984}}. * {{Citation |last=Cayley |first=Arthur |author-link= Arthur Cayley |title=On the colourings of maps |journal=Proceedings of the Royal Geographical Society |volume=1 |year=1879 |pages=259–261 |doi=10.2307/1799998 |jstor=1799998 |issue=4 |publisher=Blackwell Publishing}} * {{Citation |last1=Fritsch |first1=Rudolf |last2=Fritsch |first2=Gerda |year=1998 |title=The Four Color Theorem: History, Topological Foundations and Idea of Proof |publisher=Springer |place=New York |isbn = 978-0-387-98497-1 | others=Translated from the 1994 German original by Julie Peschke. | mr=1633950 | doi=10.1007/978-1-4612-1720-6|doi-access=free }} * {{citation|url=https://books.google.com/books?id=Mm1IAAAAYAAJ&pg=PA726|journal=[[Athenaeum (British magazine)|The Athenaeum]]|date=June 10, 1854|page=726|author=F. G.|title=Tinting Maps}}. * {{citation|last1=Gethner|first1=E.|author1-link= Ellen Gethner |last2=Springer|first2=W. M.|title=How false is Kempe's proof of the four color theorem?|journal=Congr. Numer|year=2003|volume=164|pages=159–175|zbl=1050.05049|mr=2050581}} * {{citation|first1=Ellen|last1=Gethner|author1-link= Ellen Gethner |first2=Bopanna|last2=Kalichanda|first3=Alexander S.|last3=Mentis|title=How false is Kempe's proof of the Four Color Theorem? Part II|journal=Involve|year=2009|volume=2|issue=3|pages=249–265|doi=10.2140/involve.2009.2.249|doi-access=free}} * {{Citation |last=Gonthier |first=Georges |author-link=Georges Gonthier |title=A computer-checked proof of the four colour theorem |url=https://www.cl.cam.ac.uk/~lp15/Pages/4colproof.pdf |archive-url=https://web.archive.org/web/20170908045336/http://www.cl.cam.ac.uk/~lp15/Pages/4colproof.pdf |archive-date=2017-09-08 |url-status=live |publisher=unpublished |year=2005 }} * {{Citation |last=Gonthier |first=Georges |author-link=Georges Gonthier |title=Formal Proof—The Four-Color Theorem |journal=[[Notices of the American Mathematical Society]] |volume=55 |year=2008 |url=https://www.ams.org/notices/200811/tx081101382p.pdf |archive-url=https://web.archive.org/web/20110805094909/http://www.ams.org/notices/200811/tx081101382p.pdf |archive-date=2011-08-05 |url-status=live |issue=11 |pages=1382–1393 |mr=2463991 }} * {{citation |last=Hadwiger |first=Hugo |author1-link=Hugo Hadwiger |title=Über eine Klassifikation der Streckenkomplexe |year=1943 |journal=Vierteljschr. Naturforsch. Ges. Zürich |volume=88 |pages=133–143}} * {{Citation|last=Heawood |first=P. J. |title=Map-Colour Theorem |periodical= Quarterly Journal of Pure and Applied Mathematics, Oxford |volume= 24 |year = 1890 |pages = 332–338 |author-link=Percy John Heawood}} * {{citation |title=Four Colors Do Not Suffice |first=Hud|last= Hudson |journal=The American Mathematical Monthly |volume=110 |number=5 |date=May 2003 |pages=417–423 |jstor=3647828 |doi=10.2307/3647828 }} * {{Citation|last=Kempe|first=A. B. |title=On the Geographical Problem of the Four Colours |journal = American Journal of Mathematics |volume= 2 |issue= 3|year = 1879|pages = 193–220 |author-link=Alfred Kempe |doi= 10.2307/2369235|jstor=2369235 }} * {{citation|first1=C.|last1=Magnant|first2=D. M.|last2=Martin|title=Coloring rectangular blocks in 3-space|journal=Discussiones Mathematicae Graph Theory|volume=31|issue=1|year=2011|pages=161–170|doi=10.7151/dmgt.1535 |doi-access=free }} * {{citation|first = Brendan D.|last=McKay|author-link=Brendan McKay (mathematician)|title = A note on the history of the four-colour conjecture |arxiv = 1201.2852 |year = 2012|bibcode=2012arXiv1201.2852M}} * {{citation |last = Nash-Williams |first = C. St. J. A. |author-link = Crispin Nash-Williams |journal = Journal of Combinatorial Theory |mr = 0214501 |pages = 286–301 |title = Infinite graphs—a survey |volume = 3 |issue = 3 |year = 1967 |doi=10.1016/s0021-9800(67)80077-2|doi-access = free }}. * {{Citation |last1=O'Connor |last2=Robertson |title=The Four Colour Theorem |url=http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_four_colour_theorem.html |publisher=[[MacTutor archive]] |year=1996 |access-date=2001-08-05 |archive-date=2013-01-16 |archive-url=https://web.archive.org/web/20130116053715/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_four_colour_theorem.html |url-status=dead }} * {{citation|last1=Pegg|first1=Ed Jr.|author-link=Ed Pegg, Jr.|last2=Melendez|first2=J.|last3=Berenguer|first3=R.|last4=Sendra|first4=J. R.|last5=Hernandez|first5=A.|last6=Del Pino|first6=J.|title=Book Review: The Colossal Book of Mathematics|journal=Notices of the American Mathematical Society|volume=49|issue=9|year=2002|pages=1084–1086|url=https://www.ams.org/notices/200209/rev-pegg.pdf |archive-url=https://web.archive.org/web/20030409070859/http://www.ams.org/notices/200209/rev-pegg.pdf |archive-date=2003-04-09 |url-status=live|doi=10.1109/TED.2002.1003756|bibcode=2002ITED...49.1084A}} * {{citation|last1=Reed|first1=Bruce|author1-link=Bruce Reed (mathematician)|last2=Allwright|first2=David|title=Painting the office|journal=Mathematics-in-Industry Case Studies|volume=1|year=2008|pages=1–8|url=http://www.micsjournal.ca/index.php/mics/article/view/5|access-date=2011-07-11|archive-date=2013-02-03|archive-url=https://web.archive.org/web/20130203043130/http://www.micsjournal.ca/index.php/mics/article/view/5|url-status=dead}} * {{Citation |last=Ringel |first= G.|author-link= Gerhard Ringel |title=Map Color Theorem|publisher= Springer-Verlag|location=New York–Berlin |year=1974}} * {{Citation |last1=Ringel |first1= G.|author1-link= Gerhard Ringel |last2=Youngs |first2=J. W. T. |author2-link= John William Theodore Youngs |title=Solution of the Heawood Map-Coloring Problem|periodical= Proc. Natl. Acad. Sci. USA|year=1968 |pages=438–445 |issue=2|volume = 60 |doi=10.1073/pnas.60.2.438 |pmc=225066 |pmid=16591648|bibcode = 1968PNAS...60..438R |doi-access= free}} * {{Citation |last1=Robertson |first1=Neil |author1-link=Neil Robertson (mathematician)|last2=Sanders |first2=Daniel P.|author2-link= Daniel P. Sanders |last3=Seymour |first3=Paul |author3-link=Paul Seymour (mathematician)|last4=Thomas |first4=Robin |author4-link=Robin Thomas (mathematician)|contribution=Efficiently four-coloring planar graphs |title = Proceedings of the 28th ACM Symposium on Theory of Computing (STOC 1996)|year=1996 |pages=571–575|doi = 10.1145/237814.238005 |isbn=0-89791-785-5 | mr=1427555|s2cid=14962541 }} * {{Citation |doi=10.1006/jctb.1997.1750 |last1=Robertson |first1=Neil |author1-link=Neil Robertson (mathematician)|last2=Sanders |first2=Daniel P.|author2-link= Daniel P. Sanders |last3=Seymour |first3=Paul |author3-link=Paul Seymour (mathematician)|last4=Thomas |first4=Robin |author4-link=Robin Thomas (mathematician) |title=The Four-Colour Theorem |year=1997 |periodical=J. Combin. Theory Ser. B|volume=70|pages=2–44|issue=1 | mr=1441258|doi-access=free }} * {{Citation |last1=Saaty|first1=Thomas |author-link=Thomas L. Saaty| last2=Kainen|first2=Paul|author2-link=Paul Chester Kainen| title = The Four Color Problem: Assaults and Conquest| isbn = 0-486-65092-8 |journal=Science |year=1986 |volume=202 |issue=4366 |page=424 |publisher=Dover Publications |location=New York |doi=10.1126/science.202.4366.424 |pmid=17836752 |bibcode=1978Sci...202..424S}} * {{Citation |last=Swart |first=Edward Reinier |year=1980 |title=The philosophical implications of the four-color problem |periodical=American Mathematical Monthly |volume=87 |pages=697–702 |url=http://www.maa.org/programs/maa-awards/writing-awards/the-philosophical-implications-of-the-four-color-problem |doi=10.2307/2321855 |issue=9 |jstor=2321855 |publisher=Mathematical Association of America |mr=0602826 }} * {{Citation |last=Thomas |first=Robin |title=An Update on the Four-Color Theorem |periodical=[[Notices of the American Mathematical Society]] |url=https://www.ams.org/notices/199807/thomas.pdf |archive-url=https://web.archive.org/web/20000929142844/http://www.ams.org/notices/199807/thomas.pdf |archive-date=2000-09-29 |url-status=live |year=1998 |volume=45 |pages=848–859 |author-link=Robin Thomas (mathematician) |issue=7 |mr=1633714 }} * {{Citation|last=Thomas|first=Robin|author-link=Robin Thomas (mathematician)|title=The Four Color Theorem|url=http://people.math.gatech.edu/~thomas/FC/fourcolor.html|year=1995}} * {{citation|first=Heinrich|last=Tietze|author-link=Heinrich Tietze|url=https://eudml.org/doc/145224|title=Einige Bemerkungen über das Problem des Kartenfärbens auf einseitigen Flächen|trans-title=Some remarks on the problem of map coloring on one-sided surfaces|journal= Jahresbericht der Deutschen Mathematiker-Vereinigung |volume=19|year=1910|pages=155–159}} * {{citation|chapter=Recent Excluded Minor Theorems for Graphs |first=Robin|last=Thomas|author-link=Robin Thomas (mathematician) |pages=201–222 | title=Surveys in combinatorics, 1999 | mr=1725004 | doi=10.1017/CBO9780511721335 | series=London Mathematical Society Lecture Note Series | volume=267 | publisher=Cambridge University Press | location=Cambridge | isbn=0-521-65376-2 | year=1999 | editor1-last=Lamb | editor1-first=John D. | editor2-last=Preece | editor2-first=D. A.}} * {{Citation|author-link=Peter Guthrie Tait|first=P. G.|last= Tait|title=Remarks on the colourings of maps|journal=Proc. R. Soc. Edinburgh|volume=10|year=1880|pages=729|doi=10.1017/S0370164600044643}} * {{Citation |last=Wilson |first=Robin |author-link=Robin Wilson (mathematician) |title=Four Colors Suffice | publisher=Princeton University Press |place=Princeton, New Jersey |series=Princeton Science Library |year=2014 | orig-year=2002 |isbn =978-0-691-15822-8 | mr=3235839}} * {{citation | last1=Wilson | first1=Robin | last2=Watkins | first2=John J. | last3=Parks | first3=David J. | title=Graph Theory in America | publisher=Princeton University Press | publication-place=Princeton Oxford | date=2023-01-17 | isbn=978-0-691-19402-8}} {{refend}}
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