Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Four_color_theorem> ?p ?o }
- Four_color_theorem abstract "In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions.Despite the motivation from coloring political maps of countries, the theorem is not of particular interest to mapmakers. According to an article by the math historian Kenneth May (Wilson 2014, 2), “Maps utilizing only four colors are rare, and those that do usually require only three. Books on cartography and the history of mapmaking do not mention the four-color property.”Three colors are adequate for simpler maps, but an additional fourth color is required for some maps, such as a map in which one region is surrounded by an odd number of other regions that touch each other in a cycle. The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proven in the late 19th century (Heawood 1890); however, proving that four colors suffice turned out to be significantly harder. A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.The four color theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer. Appel and Haken's approach started by showing that there is a particular set of 1,936 maps, each of which cannot be part of a smallest-sized counterexample to the four color theorem. (If they did appear, you could make a smaller counter-example.) Appel and Haken used a special-purpose computer program to confirm that each of these maps had this property. Additionally, any map that could potentially be a counterexample must have a portion that looks like one of these 1,936 maps. Showing this required hundreds of pages of hand analysis. Appel and Haken concluded that no smallest counterexamples exist because any must contain, yet do not contain, one of these 1,936 maps. This contradiction means there are no counterexamples at all and that the theorem is therefore true. Initially, their proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand (Swart 1980). Since then the proof has gained wider acceptance, although doubts remain (Wilson 2014, 216–222).To dispel remaining doubt about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. Additionally, in 2005, the theorem was proven by Georges Gonthier with general purpose theorem proving software.".
- Four_color_theorem thumbnail Four_Colour_Map_Example.svg?width=300.
- Four_color_theorem wikiPageExternalLink ?IDDOC=244202.
- Four_color_theorem wikiPageExternalLink 1256049011.
- Four_color_theorem wikiPageExternalLink 1256049012.
- Four_color_theorem wikiPageExternalLink 4colproof.pdf.
- Four_color_theorem wikiPageExternalLink The_four_colour_theorem.html.
- Four_color_theorem wikiPageExternalLink thomas.pdf.
- Four_color_theorem wikiPageExternalLink tx081101382p.pdf.
- Four_color_theorem wikiPageExternalLink 5.
- Four_color_theorem wikiPageExternalLink generalizations-of-the-four-color-theorem.
- Four_color_theorem wikiPageExternalLink the-philosophical-implications-of-the-four-color-problem.
- Four_color_theorem wikiPageID "10949".
- Four_color_theorem wikiPageLength "41325".
- Four_color_theorem wikiPageOutDegree "120".
- Four_color_theorem wikiPageRevisionID "707569024".
- Four_color_theorem wikiPageWikiLink 1-planar_graph.
- Four_color_theorem wikiPageWikiLink Alfred_Kempe.
- Four_color_theorem wikiPageWikiLink Apollonian_network.
- Four_color_theorem wikiPageWikiLink Athenaeum_(British_magazine).
- Four_color_theorem wikiPageWikiLink August_Ferdinand_Möbius.
- Four_color_theorem wikiPageWikiLink Augustus_De_Morgan.
- Four_color_theorem wikiPageWikiLink Azerbaijan.
- Four_color_theorem wikiPageWikiLink Benjamin_Werner.
- Four_color_theorem wikiPageWikiLink Big_O_notation.
- Four_color_theorem wikiPageWikiLink Category:Graph_coloring.
- Four_color_theorem wikiPageWikiLink Category:Planar_graphs.
- Four_color_theorem wikiPageWikiLink Category:Theorems_in_graph_theory.
- Four_color_theorem wikiPageWikiLink Compactness_theorem.
- Four_color_theorem wikiPageWikiLink Computational_complexity_theory.
- Four_color_theorem wikiPageWikiLink Computer-assisted_proof.
- Four_color_theorem wikiPageWikiLink Connected_space.
- Four_color_theorem wikiPageWikiLink Contiguity.
- Four_color_theorem wikiPageWikiLink Coq.
- Four_color_theorem wikiPageWikiLink Counterexample.
- Four_color_theorem wikiPageWikiLink Cuboid.
- Four_color_theorem wikiPageWikiLink Daniel_P._Sanders.
- Four_color_theorem wikiPageWikiLink De_Bruijn–Erdős_theorem_(graph_theory).
- Four_color_theorem wikiPageWikiLink Discharging_method_(discrete_mathematics).
- Four_color_theorem wikiPageWikiLink Enclave_and_exclave.
- Four_color_theorem wikiPageWikiLink Euler_characteristic.
- Four_color_theorem wikiPageWikiLink First-order_logic.
- Four_color_theorem wikiPageWikiLink Five_color_theorem.
- Four_color_theorem wikiPageWikiLink Floor_and_ceiling_functions.
- Four_color_theorem wikiPageWikiLink Francis_Guthrie.
- Four_color_theorem wikiPageWikiLink Genus_(mathematics).
- Four_color_theorem wikiPageWikiLink Georges_Gonthier.
- Four_color_theorem wikiPageWikiLink Gerhard_Ringel.
- Four_color_theorem wikiPageWikiLink German_Mathematical_Society.
- Four_color_theorem wikiPageWikiLink Glossary_of_graph_theory.
- Four_color_theorem wikiPageWikiLink Graph_(discrete_mathematics).
- Four_color_theorem wikiPageWikiLink Graph_coloring.
- Four_color_theorem wikiPageWikiLink Graph_theory.
- Four_color_theorem wikiPageWikiLink Grxc3xb6tzschs_theorem.
- Four_color_theorem wikiPageWikiLink Hadwiger_conjecture_(graph_theory).
- Four_color_theorem wikiPageWikiLink Hadwiger–Nelson_problem.
- Four_color_theorem wikiPageWikiLink Heawood_conjecture.
- Four_color_theorem wikiPageWikiLink Heinrich_Heesch.
- Four_color_theorem wikiPageWikiLink Hugo_Hadwiger.
- Four_color_theorem wikiPageWikiLink Immersion_(mathematics).
- Four_color_theorem wikiPageWikiLink John_A._Koch.
- Four_color_theorem wikiPageWikiLink John_William_Theodore_Youngs.
- Four_color_theorem wikiPageWikiLink Julius_Petersen.
- Four_color_theorem wikiPageWikiLink Kaliningrad_Oblast.
- Four_color_theorem wikiPageWikiLink Kempe_chain.
- Four_color_theorem wikiPageWikiLink Kenneth_Appel.
- Four_color_theorem wikiPageWikiLink Kenneth_O._May.
- Four_color_theorem wikiPageWikiLink Klein_bottle.
- Four_color_theorem wikiPageWikiLink Kurt_Gödel.
- Four_color_theorem wikiPageWikiLink List_of_sets_of_four_countries_that_border_one_another.
- Four_color_theorem wikiPageWikiLink Lower_Peninsula_of_Michigan.
- Four_color_theorem wikiPageWikiLink MacTutor_History_of_Mathematics_archive.
- Four_color_theorem wikiPageWikiLink Magnum_opus.
- Four_color_theorem wikiPageWikiLink Map_coloring.
- Four_color_theorem wikiPageWikiLink MathOverflow.
- Four_color_theorem wikiPageWikiLink Mathematics.
- Four_color_theorem wikiPageWikiLink Microform.
- Four_color_theorem wikiPageWikiLink Möbius_strip.
- Four_color_theorem wikiPageWikiLink NP-completeness.
- Four_color_theorem wikiPageWikiLink Nakhchivan_Autonomous_Republic.
- Four_color_theorem wikiPageWikiLink Neil_Robertson_(mathematician).
- Four_color_theorem wikiPageWikiLink Non-surveyable_proof.
- Four_color_theorem wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
- Four_color_theorem wikiPageWikiLink Orientability.
- Four_color_theorem wikiPageWikiLink Paul_Seymour_(mathematician).
- Four_color_theorem wikiPageWikiLink Percy_John_Heawood.
- Four_color_theorem wikiPageWikiLink Peter_Tait_(physicist).
- Four_color_theorem wikiPageWikiLink Planar_graph.
- Four_color_theorem wikiPageWikiLink Proof_assistant.
- Four_color_theorem wikiPageWikiLink Quartic_function.
- Four_color_theorem wikiPageWikiLink RWTH_Aachen_University.
- Four_color_theorem wikiPageWikiLink Robin_Thomas_(mathematician).
- Four_color_theorem wikiPageWikiLink Snark_(graph_theory).
- Four_color_theorem wikiPageWikiLink Szilassi_polyhedron.
- Four_color_theorem wikiPageWikiLink The_Mathematical_Intelligencer.
- Four_color_theorem wikiPageWikiLink The_New_York_Times.
- Four_color_theorem wikiPageWikiLink Theorem.
- Four_color_theorem wikiPageWikiLink Time_complexity.
- Four_color_theorem wikiPageWikiLink Toroidal_polyhedron.
- Four_color_theorem wikiPageWikiLink Torus.