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On graph coloring and neighborhood size
The theorem is named after R. Leonard Brooks, who published a proof of it in 1941. A coloring with the number of colors described by Brooks' theorem is
Brooks'_theorem
Methodic assignment of colors to elements of a graph
all other cases, the bound can be slightly improved; Brooks' theorem states that Brooks' theorem: χ ( G ) ≤ Δ ( G ) {\displaystyle \chi (G)\leq \Delta
Graph_coloring
book thickness 3 and queue number 2. The graph is not 1-planar. By Brooks’ theorem, every k-regular graph (except for odd cycles and cliques) has chromatic
Brinkmann_graph
One-by-one assignment of colors to graph vertices
combinatorial games, and the proofs of other mathematical results including Brooks' theorem on the relation between coloring and degree. Other concepts in graph
Greedy_coloring
American mathematician
primarily focused on problems related to graph coloring, including work on Brooks' theorem, the Borodin–Kostochka conjecture, list critical graphs, and Read's
Landon_Rabern
On coloring the edges of graphs
In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than
Vizing's_theorem
Graph coloring with equal color classes
significantly greater than its equitable chromatic number of two. Brooks' theorem states that any connected graph with maximum degree Δ has a Δ-coloring
Equitable_coloring
which has 11 vertices but has maximum degree 5 and is not regular. By Brooks’ theorem, every k {\displaystyle k} -regular graph (except for odd cycles and
Chvátal_graph
On tangency patterns of circles
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible patterns of tangent circles among non-overlapping
Circle_packing_theorem
Number of edges touching a vertex in a graph
exactly 1. By Brooks' theorem, any graph G other than a clique or an odd cycle has chromatic number at most Δ(G), and by Vizing's theorem any graph has
Degree_(graph_theory)
Cycle graph with all opposite nodes linked
In this case, because the graph is 3-regular but not bipartite, by Brooks' theorem it has chromatic number 3. De Mier & Noy (2004) show that the Möbius
Möbius_ladder
American mathematician
He wrote a significant paper on the series of chromatic numbers and Brooks' theorem, titled Hajós graph coloring conjecture: variations and counterexamples
Paul_A._Catlin
Need to sacrifice consistency or availability in the presence of network partitions
In database theory, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store can provide
CAP_theorem
Theorem in vector calculus
Stokes' theorem, also known as the Kelvin–Stokes theorem, is a theorem in vector calculus that relates the behavior of a vector field along the edge of
Stokes'_theorem
Undirected graph
{\displaystyle n=k} vertices, or an odd-length cycle graph. This is Brooks' theorem. 2 m ≥ ( k − 1 ) n + k − 3 {\displaystyle 2m\geq (k-1)n+k-3} . 2 m
Critical_graph
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Graph with all vertices of degree 3
single graph automorphism, the identity automorphism. According to Brooks' theorem every connected cubic graph other than the complete graph K4 has a
Cubic_graph
Family of cubic graphs formed from regular and star polygons
Petersen graphs are regular graphs of degree three, so according to Brooks' theorem their chromatic number can only be two or three. More exactly: χ (
Generalized_Petersen_graph
partitioned. It equals the chromatic number of the square of the line graph. Brooks' theorem, applied to the square of the line graph, shows that the strong chromatic
Induced_matching
Cubic graph with 10 vertices and 15 edges
vertices of the same color. It has a list coloring with 3 colors, by Brooks's theorem for list colorings. The Petersen graph has chromatic index 4; coloring
Petersen_graph
Influence of local substructure of a graph on global properties
{\displaystyle G} . When G {\displaystyle G} is not an odd cycle or a clique, Brooks' theorem states that the upper bound can be reduced to Δ ( G ) {\displaystyle
Extremal_graph_theory
2013 film by Terry Gilliam
The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges.
The_Zero_Theorem
Graph with at most one crossing per edge
of an intersection graph of an appropriate drawing, it follows from Brooks' theorem that the thickness is at most one plus the local crossing number. The
1-planar_graph
Concerns 3 circles through triples of points on the vertices and sides of a triangle
Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a
Miquel's_theorem
Approximation of a function by a polynomial
Taylor's theorem, some giving explicit estimates of the approximation error of the function by its Taylor polynomial. Taylor's theorem is named after Brook Taylor
Taylor's_theorem
Relationship between derivatives and integrals
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result
Bolzano–Weierstrass_theorem
English mathematician (1916–1993)
Rowland Leonard Brooks (February 6, 1916 – June 18, 1993) was an English mathematician, known for proving Brooks's theorem on the relation between the
R._Leonard_Brooks
odd-length cycle graphs (the graphs that form the exceptional cases to Brooks' theorem) as well as the complete bipartite graphs and complete multipartite
Well-colored_graph
Russian-American mathematician
chromatic number at most Δ − 1. The conjecture, which strengthens Brooks' theorem, remains open in general; Bruce Reed proved it for sufficiently large
Alexandr_Kostochka
Theorem in calculus relating line and double integrals
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R
Green's_theorem
English mathematician
developments are Taylor's theorem and the Taylor series, essential in the infinitesimal approach of functions in specific points. Brook Taylor was born in Edmonton
Brook_Taylor
Assignment of colors to edges of a graph
adjacent vertices. It has been conjectured (combining Vizing's theorem and Brooks' theorem) that any graph has a total coloring in which the number of colors
Edge_coloring
Concept in probability theory
In probability theory, Kolmogorov's three-series theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite
Kolmogorov's three-series theorem
Kolmogorov's_three-series_theorem
Principle relating genetic variance to fitness
Fisher's fundamental theorem of natural selection is an idea about genetic variance in population genetics developed by the statistician and evolutionary
Fisher's fundamental theorem of natural selection
Fisher's_fundamental_theorem_of_natural_selection
Soviet Ukrainian mathematician (1937–2017)
maximum cliques in graphs.[V74] He also proved a stronger version of Brooks' theorem that applies to list coloring. From 1976, Vizing stopped working on
Vadim_G._Vizing
Statement relating differentiable symmetries to conserved quantities
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law
Noether's_theorem
theorem, named after Jacob Levitzki, states that in a right Noetherian ring, every nil one-sided ideal is necessarily nilpotent. Levitzky's theorem is
Levitzky's_theorem
Principle in compass and straightedge constructions
In geometry, the compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these
Compass_equivalence_theorem
Mathematical theorem
and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring R. The theorem can be applied to show that any primitive
Jacobson_density_theorem
Theorem
Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory
Markov chain central limit theorem
Markov_chain_central_limit_theorem
Mathematical theorem about functions
In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively
Fourier_inversion_theorem
Theorem in theoretical computer science
database theory, the PACELC design principle is an extension to the CAP theorem. It states that in case of network partitioning (P) in a distributed computer
PACELC_design_principle
American mathematician (born 1989)
174.1.21, MR 2811613, S2CID 55567836 Pardon, John (2011), "Central limit theorems for random polygons in an arbitrary convex set", Annals of Probability
John_Pardon
Decomposition of an algebraic structure
Nevertheless, a group of results known under the general name Jordan–Hölder theorem asserts that whenever composition series exist, the isomorphism classes
Composition_series
Theorem in probability theory
In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the scaled mean of a random
Berry–Esseen_theorem
Branch of mathematics
curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite
Calculus
Theorem in Euclidean geometry
theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. This theorem refers
Mohr–Mascheroni_theorem
American mathematician (1900-1982)
Haskell Brooks Curry (/ˈhæskəl/ HAS-kəl; September 12, 1900 – September 1, 1982) was an American mathematician and computer scientist. Curry is best known
Haskell_Curry
American computer scientist
"geometry theorem machine" was the first advanced AI program, and the third AI program ever. It is a logical AI system that can prove theorems in planar
Herbert_Gelernter
American mathematician (born 1931)
named a Putnam Fellow in 1949 and 1950 and also proved the Fáry–Milnor theorem when he was only 19 years old. Milnor graduated with an A.B. in mathematics
John_Milnor
Branch of mathematics studying functions of a complex variable
Hypercomplex analysis List of complex analysis topics Monodromy theorem Riemann–Roch theorem Runge's theorem Vector calculus "Industrial Applications of Complex Analysis"
Complex_analysis
Macroeconomic trade theorem
The Stolper–Samuelson theorem is a theorem in Heckscher–Ohlin trade theory. It describes the relationship between relative prices of output and relative
Stolper–Samuelson_theorem
Theorem in formal logic
The cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus. It was originally proved
Cut-elimination_theorem
Russian mathematician (born 1966)
Polikanova, he established a measure-theoretic formulation of Helly's theorem.[PP86] In 1987, the year he began graduate studies, he published an article
Grigori_Perelman
Phenomenon in which AI achievements are reclassified as non-intelligent
it is no longer considered evidence of intelligence. Researcher Rodney Brooks similarly observed in 2002 that once systems are understood, they are often
AI_effect
Decomposition of periodic functions
differentiable. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier
Fourier_series
Mathematical fallacy
known as freshman exponentiation, the child's binomial theorem, (rarely) the schoolboy binomial theorem, or the Frobenius identity is the generally-false equation
Freshman's_dream
Branch of mathematics concerning probability
describing such behaviour are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential
Probability_theory
American mathematician (born 1941)
particularly motivating mathematical theorem. The change was prompted by a special case of the uniformization theorem, according to which, in his own words:
Dennis_Sullivan
Mathematics award
first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts
Fields_Medal
Property of a partially ordered set
as the intermediate value theorem, the Bolzano–Weierstrass theorem, the extreme value theorem, and the Heine–Borel theorem. It is usually taken as an
Least-upper-bound_property
Concept in probability theory
Publications, 1986, Theorem 1B. Beaver, Robert J.; Beaver, Barbara M. (2005). Introduction to Probability and Statistics. Thomson Brooks/Cole. p. 159. Schervish
Law_of_total_probability
British mathematician (1916–2000)
first paper dealt with squaring the square, he proved the Erdős–Stone theorem with Paul Erdős and is credited with the discovery of the first two flexagons
Arthur_Harold_Stone
Characterizes spherical triangles with fixed base and area
In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle
Lexell's_theorem
Probability theory
In probability theory, Kolmogorov's two-series theorem is a result about the convergence of random series. It follows from Kolmogorov's inequality and
Kolmogorov's two-series theorem
Kolmogorov's_two-series_theorem
Hungarian-American mathematician (1923-2005)
known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem. Bott was born in Budapest
Raoul_Bott
Mathematical method in calculus
The discrete analogue for sequences is called summation by parts. The theorem can be derived as follows. For two continuously differentiable functions
Integration_by_parts
Study of rates of change
Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation and integration are inverse
Differential_calculus
Mathematical approximation of a function
function, which become generally more accurate as n increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such
Taylor_series
Theorem in algebra mathematics
commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem — governs the interaction between the Jacobson radical of a ring (typically
Nakayama's_lemma
Nonexistence of gaps in the number line
completeness may take the form of an axiom (the completeness axiom), or may be a theorem proven from the construction. There are many forms of completeness, the
Completeness of the real numbers
Completeness_of_the_real_numbers
Mathematical transform that expresses a function of time as a function of frequency
sufficient regularity and decay properties is given by the Fourier inversion theorem, i.e., Inverse transform The functions f {\displaystyle f} and f ^ {\displaystyle
Fourier_transform
developed the theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws. Enheduanna
List of women in the Heritage Floor
List_of_women_in_the_Heritage_Floor
Bijective holomorphic function with a holomorphic inverse
complex plane is biholomorphic to the unit disc (this is the Riemann mapping theorem). The situation is very different in higher dimensions. For example, open
Biholomorphism
instances when the two notions coincide—this is exemplified by Levitzky's theorem. The notion of a nilpotent ideal, although interesting in the case of commutative
Nilpotent_ideal
Pathological behavior by an apportionment rule
can resolve observed paradoxes. However, as shown by the Balinski–Young theorem, it is not always possible to provide a perfectly fair resolution that
Apportionment_paradox
Integral of a comparatively larger force over a short time interval
t1 to t2. This is often called the impulse–momentum theorem (analogous to the work–energy theorem). As a result of the previous result, an impulse may
Impulse_(physics)
Russian-French mathematician
topological restrictions (such as the Cheeger–Gromoll soul theorem or Cartan–Hadamard theorem) on geodesically complete Riemannian manifolds of positive
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Mathematical relation consisting of a multi-variable function equal to zero
Some equations do not admit an explicit solution. The implicit function theorem provides conditions under which some kinds of implicit equations define
Implicit_function
Israeli theoretical physicist
quantum field theory, the a-theorem, conjectured in 1988 by John Cardy. Cardy's conjecture was a generalization of the c-theorem by Alexander Zamolodchikov
Zohar_Komargodski
American actor (born 1970)
Max DeCosta. He also appeared in the science fiction movie The Zero Theorem in 2013, directed by Terry Gilliam. That same year, Damon appeared in a
Matt_Damon
Property of geometry, also used to generalize the notion of "distance" in metric spaces
Euclidean geometry and some other geometries, the triangle inequality is a theorem about vectors and vector lengths (norms): ‖ u + v ‖ ≤ ‖ u ‖ + ‖ v ‖ , {\displaystyle
Triangle_inequality
Chinese-American mathematician (born 1949)
partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors
Shing-Tung_Yau
Mathematics of real numbers and real functions
is an upper bound that is smaller than all of the others. Most of the theorems that are proved in real analysis rely on completeness in one way or another
Real_analysis
Theoretically optimal hypothesis test
Casella, G.; Berger, R.L. (2008), Statistical Inference, Brooks/Cole. ISBN 0-495-39187-5 (Theorem 8.3.17) Ferguson, T. S. (1967). "Sec. 5.2: Uniformly most
Uniformly_most_powerful_test
Second-order partial differential equation
{\displaystyle u} is harmonic in D {\displaystyle D} , then the divergence theorem implies the compatibility condition ∫ ∂ D ∂ u ∂ ν d S = 0. {\displaystyle
Laplace's_equation
Largest and smallest value taken by a function at a given point
Transcendentals (6th ed.). Brooks/Cole. ISBN 978-0-495-01166-8. Larson, Ron; Edwards, Bruce H. (2009). Calculus (9th ed.). Brooks/Cole. ISBN 978-0-547-16702-2
Maximum_and_minimum
Transcendentals (6th ed.). Brooks/Cole. ISBN 978-0-495-01166-8. Larson, Ron; Edwards, Bruce H. (2009). Calculus (9th ed.). Brooks/Cole. ISBN 978-0-547-16702-2
Glossary_of_calculus
Process of energy transfer to an object via force application through displacement
be integrated over time to obtain a total distance, by the fundamental theorem of calculus, the total work along a path is similarly the time-integral
Work_(physics)
Topics referred to by the same term
Wiktionary, the free dictionary. Foster may refer to: Foster (surname) Foster Brooks (1912–2001), American actor Foster Moreau (born 1997), American football
Foster
Branch of mathematics
of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained
Geometry
Elementary particle involved with rest mass
also seemed to predict known massive particles as massless. Goldstone's theorem, relating to continuous symmetries within some theories, also appeared
Higgs_boson
American mathematician and billionaire (1938–2024)
California, Berkeley alumni Plateau's problem Simons' formula Simons' theorem Coy, Peter (April 11, 2019). "Meet Marilyn Simons, the Bricklayer's Daughter
Jim_Simons
Yuri Matiyasevich completing the theorem in 1970. The theorem is now known as Matiyasevich's theorem or the MRDP theorem. Optimal design In the design of
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Hypothesis on the equivalence of tax vs. debt financing
equivalence proposition (also known as the Ricardo–de Viti–Barro equivalence theorem) is an economic hypothesis holding that consumers are forward-looking and
Ricardian_equivalence
whether computers could calculate such possibilities; Gödel's incompleteness theorems; in 1974 the Arecibo Ionospheric Observatory found the Hulse–Taylor binary
List_of_Equinox_episodes
Peter Lax, 99, Hungarian-born American mathematician (Lax equivalence theorem, Lax–Friedrichs method), Abel Prize laureate (2005), cardiac amyloidosis
Deaths_in_May_2025
Borel–Carathéodory theorem Corona theorem Hadamard three-circle theorem Hardy space Hardy's theorem Maximum modulus principle Nevanlinna theory Paley–Wiener theorem Phragmén-Lindelöf
List of complex analysis topics
List_of_complex_analysis_topics
Norwegian international mathematics prize
Abel Prize?—Millennium Mathematics Project & Isaac Newton Institute Sir Faltings Wins 2026 Abel Prize (Faltings' theorem)—American Mathematical Society
Abel_Prize
BROOKS THEOREM
BROOKS THEOREM
Girl/Female
American, Arabic, Australian, British, Christian, English, French, Indian, Jamaican
A Small Fresh Water Stream; A Brook; A Stream; Breaking Forth; Dweller by the Brook; Lover
Surname or Lastname
English
English : variant of Brook, which preserves the Old English genitive case (i.e. ‘of the brook’).
Girl/Female
Christian & English(British/American/Australian)
The Brook
Surname or Lastname
English
English : variant spelling of Brook, which preserves a trace of the Old English dative singular case, originally used after a preposition (e.g. ‘at the brook’).In 1650, Robert and Mary Mainwaring Brooke brought ten children and a number of servants with them from England to MD, where Robert became governor. Although the fourteen known contemporary Brooke immigrants in VA included Robert’s brothers Richard and Humphrey, the relationships of the others are unknown. Brooke family memorials remain in the Anglican church at Whitchurch, Hampshire, England.
Boy/Male
English American
Brook; stream.
Male
English
English surname transferred to forename use, BROOKS means "of the brook."
Boy/Male
English
Near the Stream; Brook
Boy/Male
British, English
Brook; Stream; Near the Stream
Boy/Male
American, Anglo, Australian, British, Christian, English, Indian
A Small Stream; Near the Stream or Brook; From the Western Stream
Boy/Male
American, British, English
Son of Brooke
Girl/Female
English American
Water; stream. Actress Brooke Shields.
Surname or Lastname
English
English : patronymic from Rook 1.
Boy/Male
American, Australian, British, Chinese, Christian, English
Son of Brooke; Running Water; Near the Stream or Brook; Of the Brook
Surname or Lastname
English
English : from the possessive case of Brook (i.e. ‘of the brook’).Jewish (Ashkenazic) : Americanized form of one or more like-sounding Jewish surnames.Americanized spelling of German Brucks.This name was brought independently to North America from England by numerous different bearers from the 17th century onward. Among them were William Brooks, who brought the name to Scituate, MA, from Kent, England, in 1635, and Henry Brooks, who came to Woburn, MA, in or before 1649.
Surname or Lastname
English
English : patronymic from Crook 1.
Male
English
Variant spelling of English unisex Brook, BROOKE means "brook, stream."
Surname or Lastname
English
English : topographic name for someone who lived by a brook or stream, from Middle Englisk brook, Old English brÅc ‘brook’, ‘stream’.North German and Dutch : topographic name for someone who lived by a water meadow or marsh, from Low German brook, Dutch broek (cognate with German Bruch and Old English brÅc; see 1).Americanized spelling of German and Jewish Bruck or German Bruch.
Male
English
 English surname transferred to unisex forename use, from Old English broc, BROOK means "brook, stream."
Boy/Male
English
Brook; stream.
Surname or Lastname
English
English : variant spelling of Brookins.
BROOKS THEOREM
BROOKS THEOREM
BROOKS THEOREM
BROOKS THEOREM
BROOKS THEOREM
BROOKS THEOREM
BROOKS THEOREM
v. t.
To enter, write, or register in a book or list.
n.
A plant having twigs suitable for making brooms to sweep with when bound together; esp., the Cytisus scoparius of Western Europe, which is a low shrub with long, straight, green, angular branches, minute leaves, and large yellow flowers.
a.
Versed in books; having knowledge derived from books.
n. pl.
High boots, having generally a band of some kind of light-colored leather around the upper part of the leg; riding boots.
imp. & p. p.
To adorn as with a brooch.
n.
An account of books; book lore; bibliography.
n.
An implement for sweeping floors, etc., commonly made of the panicles or tops of broom corn, bound together or attached to a long wooden handle; -- so called because originally made of the twigs of the broom.
v. t.
To bear; to endure; to put up with; to tolerate; as, young men can not brook restraint.
imp. & p. p.
of Brook
v. t.
The young birds hatched at one time; a hatch; as, a brood of chickens.
n.
One who collects illustrations from various books for the decoration of one book.
a.
Inclined to brood.
v. t.
To brook; to endure.
a.
Of or pertaining to broom; overgrowing with broom; resembling broom or a broom.
n.
One who broils, or cooks by broiling.
n.
A servant at a hotel or elsewhere, who cleans and blacks the boots and shoes.
a.
Kept for breeding from; as, a brood mare; brood stock; having young; as, a brood sow.
v. t.
To sit over, cover, and cherish; as, a hen broods her chickens.