Table of Contents
109 relations: Alaska, Alfred Kempe, Angola, Apollonian network, August Ferdinand Möbius, Augustus De Morgan, Azerbaijan, Big O notation, Cabinda Province, Cartography, Compactness theorem, Computational complexity theory, Computer-assisted proof, Connected space, Coq (software), Cubic graph, Cuboid, Cylinder, Daniel P. Sanders, De Bruijn–Erdős theorem (graph theory), Discharging method (discrete mathematics), Discrete Mathematics (journal), Dorothea Blostein, Dror Bar-Natan, Earth–Moon problem, Enclave and exclave, Euler characteristic, Finite type invariant, First-order logic, Five color theorem, Floor and ceiling functions, France, Francis Guthrie, Frederick Guthrie, Genus (mathematics), Georges Gonthier, Gerhard Ringel, Glossary of graph theory, Graph (discrete mathematics), Graph coloring, Graph theory, Grötzsch's theorem, Hadwiger conjecture (graph theory), Hadwiger–Nelson problem, Heawood conjecture, Heinrich Heesch, Heinrich Tietze, Hugo Hadwiger, Immersion (mathematics), John William Theodore Youngs, ... Expand index (59 more) »
- Computer-assisted proofs
Alaska
Alaska is a non-contiguous U.S. state on the northwest extremity of North America.
See Four color theorem and Alaska
Alfred Kempe
Sir Alfred Bray Kempe FRS (6 July 1849 – 21 April 1922) was a mathematician best known for his work on linkages and the four colour theorem.
See Four color theorem and Alfred Kempe
Angola
Angola, officially the Republic of Angola, is a country on the west-central coast of Southern Africa.
See Four color theorem and Angola
Apollonian network
In combinatorial mathematics, an Apollonian network is an undirected graph formed by a process of recursively subdividing a triangle into three smaller triangles. Four color theorem and Apollonian network are planar graphs.
See Four color theorem and Apollonian network
August Ferdinand Möbius
August Ferdinand Möbius (17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer.
See Four color theorem and August Ferdinand Möbius
Augustus De Morgan
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.
See Four color theorem and Augustus De Morgan
Azerbaijan
Azerbaijan, officially the Republic of Azerbaijan, is a transcontinental country located at the boundary of Eastern Europe and West Asia.
See Four color theorem and Azerbaijan
Big O notation
Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity.
See Four color theorem and Big O notation
Cabinda Province
Cabinda (formerly called Portuguese Congo, Kabinda) is an exclave and province of Angola, a status that has been disputed by several political organizations in the territory.
See Four color theorem and Cabinda Province
Cartography
Cartography (from χάρτης chartēs, 'papyrus, sheet of paper, map'; and γράφειν graphein, 'write') is the study and practice of making and using maps.
See Four color theorem and Cartography
Compactness theorem
In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model.
See Four color theorem and Compactness theorem
Computational complexity theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other.
See Four color theorem and Computational complexity theory
Computer-assisted proof
A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Four color theorem and computer-assisted proof are computer-assisted proofs.
See Four color theorem and Computer-assisted proof
Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets.
See Four color theorem and Connected space
Coq (software)
Coq is an interactive theorem prover first released in 1989.
See Four color theorem and Coq (software)
Cubic graph
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three.
See Four color theorem and Cubic graph
Cuboid
In geometry, a cuboid is a quadrilateral-faced convex hexahedron, a polyhedron with six faces.
See Four color theorem and Cuboid
Cylinder
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
See Four color theorem and Cylinder
Daniel P. Sanders
Daniel P. Sanders is an American mathematician.
See Four color theorem and Daniel P. Sanders
De Bruijn–Erdős theorem (graph theory)
In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. Four color theorem and De Bruijn–Erdős theorem (graph theory) are graph coloring and theorems in graph theory.
See Four color theorem and De Bruijn–Erdős theorem (graph theory)
Discharging method (discrete mathematics)
The discharging method is a technique used to prove lemmas in structural graph theory.
See Four color theorem and Discharging method (discrete mathematics)
Discrete Mathematics (journal)
Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications.
See Four color theorem and Discrete Mathematics (journal)
Dorothea Blostein
Dorothea Blostein (Haken) is a Canadian computer scientist who works as a professor of computer science at Queen's University.
See Four color theorem and Dorothea Blostein
Dror Bar-Natan
Dror Bar-Natan (דרוֹר בָר-נָתָן; born January 30, 1966) is a professor at the University of Toronto Department of Mathematics, Canada.
See Four color theorem and Dror Bar-Natan
Earth–Moon problem
The Earth–Moon problem is an unsolved problem on graph coloring in mathematics. Four color theorem and Earth–Moon problem are graph coloring.
See Four color theorem and Earth–Moon problem
Enclave and exclave
An enclave is a territory that is entirely surrounded by the territory of only one other state or entity.
See Four color theorem and Enclave and exclave
Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
See Four color theorem and Euler characteristic
Finite type invariant
In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant (so named after Victor Anatolyevich Vassiliev), is a knot invariant that can be extended (in a precise manner to be described) to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities.
See Four color theorem and Finite type invariant
First-order logic
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
See Four color theorem and First-order logic
Five color theorem
The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color. Four color theorem and five color theorem are graph coloring and theorems in graph theory.
See Four color theorem and Five color theorem
Floor and ceiling functions
In mathematics, the floor function is the function that takes as input a real number, and gives as output the greatest integer less than or equal to, denoted or.
See Four color theorem and Floor and ceiling functions
France
France, officially the French Republic, is a country located primarily in Western Europe.
See Four color theorem and France
Francis Guthrie
Francis Guthrie (born 22 January 1831 in London; d. 19 October 1899 in Claremont, Cape Town) was a Cape Colony mathematician and botanist who first posed the Four Colour Problem in 1852.
See Four color theorem and Francis Guthrie
Frederick Guthrie
Frederick Guthrie FRS FRSE (15 October 1833 – 21 October 1886) was a British physicist, chemist, and academic author.
See Four color theorem and Frederick Guthrie
Genus (mathematics)
In mathematics, genus (genera) has a few different, but closely related, meanings.
See Four color theorem and Genus (mathematics)
Georges Gonthier
Georges Gonthier is a Canadian computer scientist and practitioner in formal mathematics.
See Four color theorem and Georges Gonthier
Gerhard Ringel
Gerhard Ringel (October 28, 1919 in Kollnbrunn, Austria – June 24, 2008 in Santa Cruz, California) was a German mathematician.
See Four color theorem and Gerhard Ringel
Glossary of graph theory
This is a glossary of graph theory.
See Four color theorem and Glossary of graph theory
Graph (discrete mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".
See Four color theorem and Graph (discrete mathematics)
Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
See Four color theorem and Graph coloring
Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
See Four color theorem and Graph theory
Grötzsch's theorem
In the mathematical field of graph theory, Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors. Four color theorem and Grötzsch's theorem are graph coloring, planar graphs and theorems in graph theory.
See Four color theorem and Grötzsch's theorem
Hadwiger conjecture (graph theory)
In graph theory, the Hadwiger conjecture states that if G is loopless and has no K_t minor then its chromatic number satisfies It is known to be true for The conjecture is a generalization of the four-color theorem and is considered to be one of the most important and challenging open problems in the field. Four color theorem and Hadwiger conjecture (graph theory) are graph coloring.
See Four color theorem and Hadwiger conjecture (graph theory)
Hadwiger–Nelson problem
In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distance 1 from each other have the same color. Four color theorem and Hadwiger–Nelson problem are graph coloring.
See Four color theorem and Hadwiger–Nelson problem
Heawood conjecture
In graph theory, the Heawood conjecture or Ringel–Youngs theorem gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus. Four color theorem and Heawood conjecture are graph coloring and theorems in graph theory.
See Four color theorem and Heawood conjecture
Heinrich Heesch
Heinrich Heesch (June 25, 1906 – July 26, 1995) was a German mathematician.
See Four color theorem and Heinrich Heesch
Heinrich Tietze
Heinrich Franz Friedrich Tietze (August 31, 1880 – February 17, 1964) was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers.
See Four color theorem and Heinrich Tietze
Hugo Hadwiger
Hugo Hadwiger (23 December 1908 in Karlsruhe, Germany – 29 October 1981 in Bern, Switzerland) was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.
See Four color theorem and Hugo Hadwiger
Immersion (mathematics)
In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective.
See Four color theorem and Immersion (mathematics)
John William Theodore Youngs
John William Theodore Youngs (usually cited as J. W. T. Youngs, known as Ted Youngs; 21 August 1910 Bilaspur, Chhattisgarh, India – 20 July 1970 Santa Cruz, California) was an American mathematician.
See Four color theorem and John William Theodore Youngs
Julius Petersen
Julius Peter Christian Petersen (16 June 1839, Sorø, West Zealand – 5 August 1910, Copenhagen) was a Danish mathematician.
See Four color theorem and Julius Petersen
Kaliningrad Oblast
Kaliningrad Oblast (translit) is the westernmost federal subject of the Russian Federation, in Central and Eastern Europe.
See Four color theorem and Kaliningrad Oblast
Kempe chain
In mathematics, a Kempe chain is a device used mainly in the study of the four colour theorem. Four color theorem and Kempe chain are graph coloring.
See Four color theorem and Kempe chain
Kenneth Appel
Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana–Champaign, solved one of the most famous problems in mathematics, the four-color theorem.
See Four color theorem and Kenneth Appel
Kenneth O. May
Kenneth O. May (July8, 1915December 1977) was an American mathematician and historian of mathematics, who developed May's theorem.
See Four color theorem and Kenneth O. May
Klein bottle
In mathematics, the Klein bottle is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.
See Four color theorem and Klein bottle
Kurt Gödel
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher.
See Four color theorem and Kurt Gödel
Lie algebra
In mathematics, a Lie algebra (pronounced) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity.
See Four color theorem and Lie algebra
Loop (graph theory)
In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself.
See Four color theorem and Loop (graph theory)
MacTutor History of Mathematics Archive
The MacTutor History of Mathematics Archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland.
See Four color theorem and MacTutor History of Mathematics Archive
Map coloring
In cartographic design, map coloring is the act of choosing colors as a form of map symbol to be used on a map.
See Four color theorem and Map coloring
Masterpiece
A masterpiece, magnum opus, or paren) in modern use is a creation that has been given much critical praise, especially one that is considered the greatest work of a person's career or a work of outstanding creativity, skill, profundity, or workmanship. Historically, a "masterpiece" was a work of a very high standard produced to obtain membership of a guild or academy in various areas of the visual arts and crafts.
See Four color theorem and Masterpiece
Mathematical proof
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.
See Four color theorem and Mathematical proof
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Four color theorem and Mathematics
MathOverflow
MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians.
See Four color theorem and MathOverflow
Möbius strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist.
See Four color theorem and Möbius strip
Microform
A microform is a scaled-down reproduction of a document, typically either photographic film or paper, made for the purposes of transmission, storage, reading, and printing.
See Four color theorem and Microform
Missouri
Missouri is a landlocked state in the Midwestern region of the United States.
See Four color theorem and Missouri
Nakhchivan Autonomous Republic
The Nakhchivan Autonomous Republic (Naxçıvan Muxtar Respublikası) is a landlocked exclave of the Republic of Azerbaijan.
See Four color theorem and Nakhchivan Autonomous Republic
Neil Robertson (mathematician)
George Neil Robertson (born November 30, 1938) is a mathematician working mainly in topological graph theory, currently a distinguished professor emeritus at the Ohio State University.
See Four color theorem and Neil Robertson (mathematician)
Nevada
Nevada is a landlocked state in the Western region of the United States.
See Four color theorem and Nevada
Non-surveyable proof
In the philosophy of mathematics, a non-surveyable proof is a mathematical proof that is considered infeasible for a human mathematician to verify and so of controversial validity.
See Four color theorem and Non-surveyable proof
Notices of the American Mathematical Society
Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.
See Four color theorem and Notices of the American Mathematical Society
NP-completeness
In computational complexity theory, a problem is NP-complete when.
See Four color theorem and NP-completeness
Open set
In mathematics, an open set is a generalization of an open interval in the real line.
See Four color theorem and Open set
Orientability
In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise".
See Four color theorem and Orientability
Overseas France
Overseas France (France d'outre-mer, also France ultramarine) consists of 13 French territories outside Europe, mostly the remains of the French colonial empire that remained a part of the French state under various statuses after decolonization.
See Four color theorem and Overseas France
Paul Seymour (mathematician)
Paul D. Seymour (born 26 July 1950) is a British mathematician known for his work in discrete mathematics, especially graph theory.
See Four color theorem and Paul Seymour (mathematician)
Percy John Heawood
Percy John Heawood (8 September 1861 – 24 January 1955) was a British mathematician, who concentrated on graph colouring.
See Four color theorem and Percy John Heawood
Peter Guthrie Tait
Peter Guthrie Tait (28 April 18314 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics.
See Four color theorem and Peter Guthrie Tait
Philip Franklin
Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis.
See Four color theorem and Philip Franklin
Pie chart
A pie chart (or a circle chart) is a circular statistical graphic which is divided into slices to illustrate numerical proportion.
See Four color theorem and Pie chart
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. Four color theorem and planar graph are planar graphs.
See Four color theorem and Planar graph
Proof assistant
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration.
See Four color theorem and Proof assistant
Proof without words
In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
See Four color theorem and Proof without words
Quartic function
In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
See Four color theorem and Quartic function
Robin Thomas (mathematician)
Robin Thomas (August 22, 1962 – March 26, 2020) was a mathematician working in graph theory at the Georgia Institute of Technology.
See Four color theorem and Robin Thomas (mathematician)
RWTH Aachen University
RWTH Aachen University, in German Rheinisch-Westfälische Technische Hochschule Aachen, is a German public research university located in Aachen, North Rhine-Westphalia, Germany.
See Four color theorem and RWTH Aachen University
Snark (graph theory)
In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three colors. Four color theorem and snark (graph theory) are graph coloring.
See Four color theorem and Snark (graph theory)
Sphere
A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.
See Four color theorem and Sphere
Szilassi polyhedron
In geometry, the Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces.
See Four color theorem and Szilassi polyhedron
The Athenaeum (British magazine)
The Athenæum was a British literary magazine published in London, England, from 1828 to 1921.
See Four color theorem and The Athenaeum (British magazine)
The Mathematical Intelligencer
The Mathematical Intelligencer is a mathematical journal published by Springer Science+Business Media that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.
See Four color theorem and The Mathematical Intelligencer
The New York Times
The New York Times (NYT) is an American daily newspaper based in New York City.
See Four color theorem and The New York Times
Theorem
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.
See Four color theorem and Theorem
Tietze's graph
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges.
See Four color theorem and Tietze's graph
Time complexity
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm.
See Four color theorem and Time complexity
Toroidal polyhedron
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a -holed torus), having a topological genus of 1 or greater.
See Four color theorem and Toroidal polyhedron
Torus
In geometry, a torus (tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle.
See Four color theorem and Torus
Transitive relation
In mathematics, a binary relation on a set is transitive if, for all elements,, in, whenever relates to and to, then also relates to.
See Four color theorem and Transitive relation
Triangle-free graph
In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges.
See Four color theorem and Triangle-free graph
Triangulation (geometry)
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Four color theorem and triangulation (geometry) are planar graphs.
See Four color theorem and Triangulation (geometry)
United States
The United States of America (USA or U.S.A.), commonly known as the United States (US or U.S.) or America, is a country primarily located in North America.
See Four color theorem and United States
University College London
University College London (branded as UCL) is a public research university in London, England.
See Four color theorem and University College London
University of Illinois Urbana-Champaign
The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States.
See Four color theorem and University of Illinois Urbana-Champaign
Vertex (graph theory)
In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
See Four color theorem and Vertex (graph theory)
W. W. Rouse Ball
Walter William Rouse Ball (14 August 1850 – 4 April 1925), known as W. W.
See Four color theorem and W. W. Rouse Ball
Wolfgang Haken
Wolfgang Haken (June 21, 1928 – October 2, 2022) was a German American mathematician who specialized in topology, in particular 3-manifolds.
See Four color theorem and Wolfgang Haken
1-planar graph
In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point, where it crosses a single additional edge. Four color theorem and 1-planar graph are planar graphs.
See Four color theorem and 1-planar graph
See also
Computer-assisted proofs
- Boolean Pythagorean triples problem
- Computer-assisted proof
- Connect Four
- Four color theorem
- Goldbach's weak conjecture
- Kazhdan's property (T)
- Keller's conjecture
- Kepler conjecture
- Kolmogorov–Arnold–Moser theorem
- Minimum-weight triangulation
- Mutually unbiased bases
- Optimal solutions for the Rubik's Cube
- Projective plane
- Robbins algebra
- SIC-POVM
- Schur's theorem
- Sign sequence
- Sudoku
References
Also known as 4 color map problem, 4 color problem, 4 color theorem, 4 colour map problem, 4 colour theorem, 4-color conjecture, 4-color problem, 4-color theorem, 4-colors theorem, 4CT, Four Color Conjecture, Four Color Problem, Four Color Theory, Four Colour Theorem, Four color map problem, Four color map theorem, Four colour map problem, Four colour map theorem, Four colour problem, Four-Color Map Theorem, Four-Color Maps, Four-Color Theorem, Four-Colour Map Problem, Four-Colour Theorem, Four-color conjecture, Four-color map, Four-color map problem, Four-color problem, Four-colour map, Four-colour problem, History of the four color theorem, Map color problem, Map coloring problem, Map-coloring problem, Minimum number of map colors, Proof of the 4 color theorem, Seven colour theorem, The Four-Color map Theorem.