Home  - Theorems_And_Conjectures - Four Colour Theorem

e99.com Bookstore
 Images Newsgroups
 Page 2     21-40 of 88    Back | 1  | 2  | 3  | 4  | 5  | Next 20

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

21. Sci.math FAQ: The Four Colour Theorem
Subject sci.math FAQ The four colour theorem. 429567. N. Robertson, D. Sanders,P. Seymour, R. Thomas The four colour theorem Preprint, February 1994.
http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/fourcolour.html
Note from archivist@cs.uu.nl : This page is part of a big collection of Usenet postings, archived here for your convenience. For matters concerning the content of this page , please contact its author(s); use the source , if all else fails. For matters concerning the archive as a whole, please refer to the archive description or contact the archivist.
##### Subject: sci.math FAQ: The Four Colour Theorem
This article was archived around: 17 Feb 2000 22:52:04 GMT
##### All FAQs in Directory: sci-math-faq All FAQs posted in: sci.math Source: Usenet Version
Archive-name: sci-math-faq/fourcolour Last-modified: February 20, 1998 Version: 7.5 http://www.cs.unb.ca/~alopez-o Assistant Professor Faculty of Computer Science University of New Brunswick

 22. Four Colour Map Theorem From FOLDOC four colour theorem . four colour map theorem. mathematics, application (Or four colour theorem ) The theorem stating that ifhttp://csai03.is.noda.sut.ac.jp/foldoc/foldoc.cgi?four colour theorem

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

24. Sci.math FAQ: The Four Colour Theorem
sci.math FAQ The four colour theorem. 21, 1977, pp. 429567. N. Robertson, D. Sanders,P. Seymour, R. Thomas The four colour theorem Preprint, February 1994.
http://www.uni-giessen.de/faq/archiv/sci-math-faq.fourcolour/msg00000.html
Index
##### sci.math FAQ: The Four Colour Theorem
http://www.cs.unb.ca/~alopez-o Assistant Professor Faculty of Computer Science University of New Brunswick

25. Four Colour Theorem
four colour theorem. Start your search on four colour theorem. Othereducational search engines Ask Jeeves for Kids Britannica
http://www.virtualology.com/virtualpubliclibrary/hallofeducation/Mathematics/Fou
You are in: Virtual Public Library Hall of Education Mathematics Four Colour Theorem
##### Start your search on Four Colour Theorem
Other educational search engines:
Ask Jeeves for Kids
Britannica.com CyberSleuth Kids Education World ... Yahooligans
Unauthorized Site: This site and its contents are not affiliated, connected, associated with or authorized by the individual, family, friends, or trademarked entities utilizing any part or the subjects entire name. Any official or affiliated sites that are related to this subject will be hyper linked below upon submission and Virtualology's review. 2000 by Virtualology TM . All rights reserved.
Virtualology TM Search:
e-mail us Editing Sponsor Editing Sponsors review and select all student work for publishing. To learn more about our editing sponsor program click here. Published Students Primary
Secondary

College

...
Technical

26. 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
The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: four colour map theorem Next: Fourier transform
##### four colour theorem
four colour map theorem

27. 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
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
##### four colour map 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

28. 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
 Name: rhonda Who is asking: Student Level: Secondary Question: is there an actual equation for the four colour map theorem? i cannot find it anywhere!! if so can you give a breif description on how it works!! Thank you 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 Go to Math Central To return to the previous page use your browser's back button.

29. Citations: A New Proof Of The Four Colour Theorem - Robertson, Sanders, Seymour,
N. Robertson, DP Sanders, PD Seymour and R. Thomas, A new proof of the four colourtheorem, Electron. Res. A new proof of the fourcolour theorem. Electron.
http://citeseer.nj.nec.com/context/1083701/372465
 7 citations found. Retrieving documents... N. Robertson, D. P. Sanders, P. Seymour and R. Thomas, A new proof of the four-colour theorem , Electronic Research Announcements of the American Mathematical Society, vol. 2 (1996), 1725. Home/Search Document Details and Download Summary Related Articles ... Check This paper is cited in the following contexts: On Local Transformation of Polygons with Visibility.. - Hernando, Houle, Hurtado (Correct) ....the Platonic solids. In recent years, the use of computers has allowed the investigation of structures far more complex than those considered by the ancients. In graph theory, the only proofs yet known of the famous Four Color Theorem have been obtained by means of computer enumeration of cases Also, a general purpose program for computing automorphism groups of graphs and digraphs developed by Brendan McKay, Nauty, has been used to prove a number of graph theoretic results, most notably C. Hernando and F. Hurtado partially supported by CUR Gen. Cat . 1999SGR00356 and MEC DGES SEUID .... N. Robertson, D. P. Sanders, P. D. Seymour and R. Thomas, `

30. Four-Coloring Six-Regular Graphs On The Torus - Collins, Hutchinson (ResearchInd
colorable (context) Appel, Haken - 1976 87 Introduction to Graph Theory (context)- West - 1996 20 The four colour theorem (context) - Robertson, Sanders et
http://citeseer.nj.nec.com/collins99fourcoloring.html
 Four-Coloring Six-Regular Graphs On The Torus (1999) (Make Corrections) (1 citation) Karen L. Collins, Joan P. Hutchinson Home/Search Context Related View or download: wesleyan.edu/public foursixsent3.ps Cached: PS.gz PS PDF DjVu ... Help From: wesleyan.edu/vita (more) Homepages: K.Collins J.Hutchinson HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: this paper we focus on the torus and on ostensibly the most dicult case when the graph is a six-regular triangulation; in [28] Thomassen asks for a characterization of the non-4-colorable, 6-regular graphs on the torus. A theorem of Altshuler [4] shows that every 6regular toroidal graph can be represented as a 6-regular shifted rectangular grid on the torus; see Figure 2. A shift of one is the same as an unshifted grid. This allows us to focus rst on 6-regular grids and then to extend our... (Update) Context of citations to this paper: More ...can be 3 colored. This result is attributed to Heawood [16] though it could equally well be attributed to Kempe [20] As conjectured in , these graphs embedded on orientable surfaces with sufficiently large width can always be 4 colored [19] and so a 4 color extension Cited by: More Extending Colorings of Locally Planar Graphs - December Michael Albertson (Correct) Active bibliography (related documents): More All Long cycles in graphs on a fixed surface - Böhme, Mohar, al. (1999)

31. ColourTheory
The four colour theorem (or the Four Color Theorem). Mathematicians Nomore so than in the area of the four colour theorem. This
 Maps and Mapping What is a Map Map Distortions How to build maps Using a GPS survey ... RGB and CYMK Colours The Four Colour Theorem (or the Four Color Theorem) Mathematicians and map makers share a lot of common ground. No more so than in the area of the four colour theorem. This theorem simply states that any map in a single plane can be coloured using four-colours in such a way that any regions sharing a common boundary (other than a single point) do not share the same colour. The theorem was first propounded by F Guthrie in 1853. Fallacious proofs have come and gone starting with Kempe in 1879 and Tait an 1880. In 1977 K. Appel and W. Haken used computer assistance to test many different combinations to effectively prove that four colours was all that was required in all instances. Since then, it may be that a mathematical proof has, at last, been arrived at. So, if we know that we can colour any map using just four colours how to we go about it. A little though would indicate that the problem is not straightforward. Simply starting with a random colour and an arbitrary polygon would soon lead to an impasse when the process met an area bounded by more than three other areas yet to be coloured. Kempe is credited with first recording that, when tackling a map of national boundaries, those with three or fewer neighbours presented no problems. His solution was to ignore (temporarily remove from the map) those countries with three or fewer neighbours. This process will immediately simplify the remainder of the map and can be repeated until only countries with three or fewer neighbours remain. The remaining areas can then be coloured. Then the missing countries can be restored in reverse order to their removal and coloured as the process proceeds. This effective procedure is know as Kempe transformations.

32. Map Colours
Colour and Maps. The four colour theorem says that the areas of a mapcan be coloured in using just four colours. Ignore the minimalists
 Maps and Mapping What is a Map Map Distortions How to build maps Using a GPS survey ... RGB and CYMK Colours Colour and Maps The four colour theorem says that the areas of a map can be coloured in using just four colours. Ignore the minimalists - colour has an important part to play in communicating information held on a map. Wise colour choice and colour usage can enhance the experience of your map users. The poor use of colour can degrade you map and make it difficult to use. Good colour choice like any design issue seems to demand a little flair and it is difficult to define hard a fast rules. Review other maps you have seen that have a similar purpose to your map. Try and decide where the use of colour has enhanced the objectives and where it has detracted from the map. This may help you decide upon how to apply colour to your specific map. If your map is likely to be photocopied or faxed (perhaps a how to find us map) then this should be taken into account when designing it. A monochrome line drawing might work better than a map with coloured areas and text. Reds and blacks fax well, blues and greens do not. If place and location names or any other form of text are an important attribute of your map then your colour scheme should take this into account. Colour contrasts could become very important to ensure that your text stands out on the relevant background areas.

33. Maths Thesaurus: Four Colour Theorem
Home four colour theorem Any network of points and lines in a plane can be colouredin using no more than four colours, in such a way that no two adjacent
http://thesaurus.maths.org/dictionary/map/word/3028
 Four colour theorem Any network of points and lines in a plane can be coloured in using no more than four colours, in such a way that no two adjacent regions have the same colour. Find similar words More general: Compare with: Defined earlier: Theorem Seven colour theorem Four color problem New search: Age: 19 Choose Language and Age Make a suggestion nrich@damtp.cam.ac.uk

34. Count On
emphasise the changes due to the morphing (A large version of the tiling is downloadableas an Acrobat PDF file as MT7.pdf) The four colour theorem A tiling

 35. LinuxGuruz Foldoc Page Affordable Web Hosting. Cheap Web Hosting. Was our site helpfull? Want to make adonation? \$. LinuxGuruz Foldoc. four colour theorem . four colour map theorem.http://foldoc.linuxguruz.org/foldoc.php?four colour theorem

36. Claim Of Proof To Four-Color Theorem
The recent announcement by two American computer scientists that they have a proofof the four colour theorem, although they certainly have not published a
http://www.lawsofform.org/gsb/nature.html
##### Claim of Proof to Four-Color Theorem
By G. Spencer-Brown To the Editors of Nature , 4 Little Essex Street, London W C 2 England
copies to other interested journals From G Spencer-Brown, 2 St Peters St, Castle Hill, Cambridge England
17 December 1976 Sirs The recent announcement by two American computer scientists that they have a proof of the four colour theorem, although they certainly have not published a proof, coupled with the fact that they are widely reported as saying they believe that no simple or elegant proof of this theorem is possible, prompts me to refer to the work of me and my brother, the late D J Spencer-Brown, on this theorem as early as 1960-1964. As reported in 1969 [ ], we found during this period an extremely elegant way of expressing the four-colour conjecture (as it then was) which, if verified, would lead to a correspondingly elegant proof. As is well known, the difficulty of the foul colour problem stems from the fact that the Heawood formulae [ ], say Hmin, Hmax, giving the minimum and maximum values for the chromatic numbers of surfaces (Sg) of connectivity g, give Hmin = Hmax = [(1/2)(7 + (24g - 23)^(1/2) )] for g > 1

37. Four Color Theorem
the book. The MacTutor History of Mathematics archive at Saint Andrewshas a nice article on the four colour theorem. A summary
http://grail.cba.csuohio.edu/~somos/4ct.html
##### Four Color Theorem
Around 1998 Paul Kainen and I worked on an approach to the Four Color Theorem. He is a co-author of a book on this topic reprinted by Dover Publications. AUTHOR Saaty, Thomas L. TITLE The four-color problem : assaults and conquest / Thomas L. Saaty and Paul C. Kainen. PUBLISH INFO New York : Dover Publications, 1986. DESCRIPT'N vi, 217 p. : ill. ; 21 cm. NOTE Includes bibliographical references (p. 197-211) and index. SUBJECTS Four-color problem. LC NO QA612.19 .S2 1986. DEWEY NO 511/.5 19. OCLC # 12975758. ISBN 0486650928 (pbk.) : \$6.00. AUTHOR Saaty, Thomas L. TITLE The four-color problem : assaults and conquest / Thomas L. Saaty and Paul C. Kainen. PUBLISHER New York : McGraw-Hill International Book Co., c1977. DESCRIPTION ix, 217 p. : ill. ; 25 cm. NOTES Bibliography: p. 197-211. Includes index. OCLC NO. 3186236. ISBN 0070543828 : \$23.00. We take a pair of triangulations of a polygon and four color the vertices such that no two of the same color are connected by an edge of the triangulations. Polygon triangulations are easy to represent using data structures and the topological considerations of planarity are avoided. This turns the problem into a combinatorial one. The planarity reduces to circular order along the polygon and the non-crossing of diagonals. The history of this approach going back to Hassler Whitney and other references to this approach are in the book.

38. The Four Colour Theorem
The four colour theorem. The Four Colour errors. The four colour theoremreturned to being the Four Colour Conjecture in 1890. Percy John
http://math.5u.com/The four colour theorem.htm
Cheap Web Site Hosting
##### The four colour theorem

39. 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.
##### PAGES WEB
The Four Color Theorem
This page gives a brief summary of a new proof of the Four Color Theorem and a four-coloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas.
The Geometry Junkyard Coloring
Graph Coloring Page
by Joseph Culberson.
Robin Thomas
School of Mathematics Georgia Institute of Technology Atlanta, Georgia
Daniel P. Sanders
##### LOGICIELS - SOFTWARES
four at ftp.math.gatech.edu
This directory contains the programs and data that serve as supplements to the paper `The Four-Colour Theorem' by N. Robertson, D. P. Sanders, P. D. Seymour and R. Thomas, J. Combin. Theory Ser. B 70 (1997), 2-44. They naturally fall into two parts, Reducibility and Discharging.
Graph Coloring Programs
Joseph Culberson Department of Computing Science University of Alberta Edmonton, Alberta, Canada T6G 2H1
Network Resources for Coloring a Graph
##### DOCUMENTS - PAPERS
four colors survey
A new proof of the four-colour theorem
Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas
couleurs
Bienvenue chez Sylvain Poirier
##### JOURNAUX - LETTERS
Electronic Research Announcements
of the American Mathematical Society A new proof of the four-colour theorem
##### QUESTIONS - FAQ
sci.math FAQ: The Four Colour Theorem

40. University Of Wuppertal - Dep. Of Mathematics - Poster
imaginary maps. It has taken more than 100 years before a correctproof for the four colour theorem has been found. The proof by
http://www.math.uni-wuppertal.de/org/Poster/TextE.htm
##### The four colour problem
In 1852, while colouring a map representing the english counties, the british mathematician Francis Guthrie realized that only four colours where necessary to satisfy the criterion that neighbouring counties should have different colours. It turns out that this is true for any (real or imaginary) map. The poster shows such a colouring for the countries of Europe and, in small, for three other imaginary maps. It has taken more than 100 years before a correct proof for the four colour theorem has been found. The proof by Appel and Haken in 1976 has solicited much of a controversial discussion since it heavily relies on computer calculations. These are so extensive that humans cannot verify them "by hand". Consequently, proving the four colour theorem correct also means proving that the program is implemented correctly and that the computer works correctly. Instead of taking Europe and its countries, we could illustrate the four colour theorem with Germany and its regions. This can be found at MathePrisma (in German). There you can also colour some other maps on your own and develop strategies to get the right colouring fast.

 Page 2     21-40 of 88    Back | 1  | 2  | 3  | 4  | 5  | Next 20