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Four Colour Theorem:     more detail
1. Graphs, Colourings and the Four-Colour Theorem (Oxford Science Publications) by Robert A. Wilson, 2002-03-28
2. ON EXTENDED CONGRUENCES CONNECTED WITH THE FOUR-COLOUR MAP THEOREM. by P. J. (SIGNED) HEAWOOD, 1929-01-01

lists with details

1. FourColourTheorem
four colour theorem Four color theorem (English). Search for Four colourtheorem OR Four color theorem in NRICH PLUS maths.org Google.
http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=3028

2. FourColourTheorem
four colour theorem. four colour theorem Four color theorem (English).Search for four colour theorem OR Four color theorem
http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=3028&langcod

3. Four Colour Theorem
four colour theorem. four colour theorem. The four colour theorem statesthat any planar (flat 2d) map needs only 4 colours to be coloured in.
http://www.users.globalnet.co.uk/~perry/maths/fourcolour/fourcolour.htm

Extractions: Four Colour Theorem The four colour theorem states that any planar (flat 2d) map needs only 4 colours to be coloured in. There is only one rule, adjacent regions must be in different colours. Regions that are connected at a point are not adjacent. The above image shows a skeleton map that needs colouring, and two possible colourings. There are generally many alternatives using only 4 colours, and the Four Colour theorem asks 'Is there a map that we can create that requires 5 colours?'. The first colouring is created using an agressive technique - a colour is applied to a random region, and then, again randomly, to as many regions as possible. Once exhausted, another colour is used. The second counts the regions - 12 in this case, and then creates 3 regions of each colour. This raises an important point. We can colour the maps using 5 colours, but we only NEED four. And is it possible to create a scenario where 4 colours does not seem to be enough, but there will be an different pattern that does colour the map in four. A simple proof of this theorem has eluded mathematicians for centuries, but here is a proof that the four colour theorem is true, and that there is no planar map that needs 5 or more colours.

4. About "A New Proof Of The Four Colour Theorem"
A New Proof of The four colour theorem.
http://mathforum.org/library/view/16622.html

Extractions: Visit this site: http://www.geocities.com/dharwadker/ Author: Ashay Dharwadker Description: An article presenting a proof of the four color theorem that uses group theory and Steiner systems, illustrated using a map of Madhya Pradesh and adjoining states in India. Introduction; Map Colouring; Steiner Systems; Eilenberg Modules; Hall Matchings; Riemann Surfaces; Main Construction; References. Levels: Research Languages: English Resource Types: Articles Math Topics: Group Theory Graph Theory

5. Math Forum - Ask Dr. Math
The four colour theorem Theorem 2 four colour theorem Every planar map with regionsof simple borders can be coloured with 4 colours in such a way that no

Extractions: Associated Topics Dr. Math Home Search Dr. Math Date: 8/21/96 at 7:2:31 From: Satyadeepcp Subject: Four-Colour Theorem Do we need more than 4 colors to color a 2-dimensional map? Date: 8/27/96 at 20:40:27 From: Doctor Jodi Subject: Re: Four-Colour Theorem Here's an answer to your question from the sci-math faq ( http://daisy.uwaterloo.ca/~alopez-o/math-faq/math-faq.html http://mathforum.org/dr.math/ Associated Topics

6. Bookmarks Four Colors
QUESTIONS FAQ. sci.math FAQ The four colour theorem http//www.cs.ruu.nl/wais/html/na-dir/sci-math-faq/fourcolour.html .up.

7. The Four Colour Theorem
Question is there an actual equation for the four colour map theorem? i cannotfind it anywhere!! if so can you give a breif description on how it works!!
http://mathcentral.uregina.ca/QQ/database/QQ.09.02/rhonda1.html

Extractions: Hi Rhonda, The theorem is just that, a theorem, and it proves that any map in the plane can be coloured properly with just 4 colours. That is not the same as saying that there is an efficient algorithm to 4-colour any planar map; it just assures us that it can actually be done. Thus unless your map is quite small and not too complicated it may be a very difficult task indeed to actually colour it properly with 4-colours. Cheers, Penny

8. Four Colour Map Theorem From FOLDOC
Free Online Dictionary of Computing. four colour theorem . fourcolour map theorem. mathematics, application (Or four colour
http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?four colour theorem

9. Four Colour Map Theorem From FOLDOC
Free Online Dictionary of Computing. four colour map theorem. mathematics,application (Or four colour theorem ) The theorem stating
http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?four colour map theorem

10. Mathenomicon.net : Reference : Four Colour Theorem
Mathenomicon.net, four colour theorem. The theoremstating that every planar graph has a 4colouring.
http://www.cenius.net/refer/display.php?ArticleID=fourcolourtheorem_ency

11. Mathenomicon.net : Reference : Four Colour Theorem
Mathenomicon.net, four colour theorem. noun. discounted). The Four ColourTheorem is more properly expressed in terms of graph theory
http://www.cenius.net/refer/display.php?ArticleID=fourcolourtheorem

12. Four Colour Map Theorem From FOLDOC
four colour theorem . four colour map theorem. mathematics, application (Or four colour theorem ) The theorem stating that if
http://www.swif.uniba.it/lei/foldop/foldoc.cgi?four colour theorem

13. Four Colour Map Theorem From FOLDOC
four colour theorem . four colour map theorem. mathematics, application (Or four colour theorem ) The theorem stating that if
http://www.instantweb.com/foldoc/foldoc.cgi?four colour theorem

14. Robert A Wilson Graphs Colourings And The Four Colour Theorem
Robert A Wilson Graphs Colourings and the four colour theorem. Authoror Artist Robert A Wilson. Title Graphs Colourings and the
http://www.welsh-breaks.co.uk/Robert-A-Wilson-Graphs-Colourings-and-th-920-934-7

15. Four Colour Theorem
Denis Howe dbh@doc.ic.ac.uk . Previous four colour map theorem NextFourier transform. four colour theorem. four colour map theorem.
http://burks.brighton.ac.uk/burks/foldoc/90/44.htm

16. Four Colour Map Theorem
uk . Previous fourcolour glossies Next four colour theorem. fourcolour map theorem. mathematics, application (Or four colour
http://burks.brighton.ac.uk/burks/foldoc/89/44.htm

Extractions: The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: four-colour glossies Next: four colour theorem mathematics application The proof, due to Appel and Haken, attained notoriety by using a computer to check tens of thousands of cases and is thus not humanly checkable, even in principle. Some thought that this brought the philosophical status of the proof into doubt. There are now rumours of a simpler proof, not requiring the use of a computer. See also chromatic number

17. ThinkQuest : Library : A Taste Of Mathematic
Tait addressed the Royal Society of Edinburgh on the subject and publishedtwo papers on the (what we should now call) four colour theorem.
http://library.thinkquest.org/C006364/ENGLISH/problem/four.htm

Extractions: Index Math Welcome to A Taste of Mathematics.You will find the taste of mathematics here.The history of Mathematics,famous mathematicians,cxciting knowledge,the world difficult problems and also mathematics in our life... Browsing,thinking,enjoying,and have a good time here! Visit Site 2000 ThinkQuest Internet Challenge Languages English Chinese Students fangfei Beijing No.4 High School, Beijing, China ziyan Beijing No.4 High School, Beijing, China Coaches Tife Zesps3 Szks3 Ogslnokszta3c9cych Numer 1, Beijing, China xueshun Beijing No.4 High School, Beijing, China Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

18. Computer Dictionary Definition Of Four Colour Theorem
Computer Dictionary Definition of four colour theorem. Search dictionary. Displayingall Computer dictionary definition of four colour theorem. Definition
http://www.realdictionary.com/computer/Computer/four-colour-theorem.asp

19. Four Colour Theorem @ Computer-Dictionary-Online.org
four colour theorem @ Computer Dictionary Online. a b c d e f g h i j k l mn o p q r s t u v w x y z. four colour theorem four colour map theorem
http://www.computer-dictionary-online.org/?q=four colour theorem

20. Applications Of The Four Colour Theorem Proof Technique
Time 400 PM. Title Applications of the four colour theorem Proof Technique. Thetalk begins with an overview of the four colour theorem s history and proof.
http://www.math.sunysb.edu/cal/event.php?ID=465&Date=2004-03-25

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