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Special case of graph labeling in graph theory
In graph theory, a weak coloring is a special case of a graph labeling. A weak k-coloring of a graph G = (V, E) assigns a color c(v) ∈ {1, 2, ..., k} to
Weak_coloring
Graph with directed and undirected edges
{\overrightarrow {uv}}\in A} . A weaker condition on our arcs can be applied and we can consider a weak proper k-coloring of a mixed graph to be a function
Mixed_graph
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Maximum number of disjoint dominating sets
this, note that (1) a weak 2-coloring is a domatic partition if there is no isolated vertex, and (2) any graph has a weak 2-coloring. Alternatively, (1)
Domatic_number
Planar maps require at most four colors
software. The coloring of maps can also be stated in terms of graph theory, by considering it in terms of constructing a graph coloring of the planar
Four_color_theorem
Assignment of colors to edges of a graph
edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem
Edge_coloring
On coloring infinite graphs
In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that, when
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
Conjecture in graph theory
by Stephen T. Hedetniemi in 1966, concerns the connection between graph coloring and the tensor product of graphs. This conjecture states that χ ( G × H
Hedetniemi's_conjecture
Complements of perfect graphs are perfect
the size of the largest clique equals the minimum number of colors in a coloring of the subgraph. Perfect graphs include many important graphs classes including
Perfect_graph_theorem
Non-crossing graph with vertices on outer face
length. An edge coloring with an optimal number of colors can be found in linear time based on a breadth-first traversal of the weak dual tree. Outerplanar
Outerplanar_graph
Influence of local substructure of a graph on global properties
graph has a coloring with a prescribed number of colors is known to be NP-hard. In addition to vertex coloring, other types of coloring are also studied
Extremal_graph_theory
Yellow food coloring
that certain food colorings may act as a trigger in those who are genetically predisposed, but the evidence for this effect is weak. Rumors began circulating
Tartrazine
Manually applying colour to black-and-white photographs
Hand-colouring (or hand-coloring) refers to any method of manually adding colour to a monochrome photograph, generally either to heighten the realism of
Hand-colouring_of_photographs
Planar maps require at most five colors
smaller graph with one less vertex, five-coloring that graph, and then using that coloring to determine a coloring for the larger graph in constant time
Five_color_theorem
Graph coloring related to treedepth
has the same color. A q {\displaystyle q} -centered coloring is a centered coloring with the weaker property that every connected subgraph (or equivalently
Centered_coloring
Hygiene and cosmetology involving human hair
Hair coloring is the process of adding pigment to or removing pigment from the hair shaft. Hair coloring processes may be referred to as coloring or bleaching
Hair_care
Theorem on triangulation graph colorings
result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring (described
Sperner's_lemma
3-regular graph with no 3-edge-coloring
their name is much newer, given to them by Martin Gardner in 1976. Beyond coloring, snarks also have connections to other hard problems in graph theory: writing
Snark_(graph_theory)
Branch of mathematical logic
p. 34. Simpson 2009, Theorem IV.7.7. Schmerl, James H. (2000). "Graph coloring and reverse mathematics". Mathematical Logic Quarterly. 46 (4): 543–548
Reverse_mathematics
Icing used on cakes and pastries
that would be difficult to make with a softer icing. It also takes food coloring well. Rolled fondant is very sweet but otherwise is not considered to taste
Fondant_icing
Vitamin, dietary supplement, and yellow food dye
powder. In addition to its function as a vitamin, it is used as a food coloring agent. Biosynthesis takes place in bacteria, fungi and plants, but not
Riboflavin
Weak organic acid
Citric acid is an organic compound with the formula C6H8O7. It is a colorless weak organic acid. It occurs naturally in citrus fruits. In biochemistry, it is
Citric_acid
The open coloring axiom (abbreviated OCA) is an axiom about coloring edges of a graph whose vertices are a subset of the real numbers: two different versions
Open_coloring_axiom
Chemical element with atomic number 27 (Co)
them is so small that random intergrowth of the two is common. Cobalt is a weakly reducing metal that is protected from oxidation by a passivating oxide film
Cobalt
Partition of a graph's nodes into cliques
chromatic number (minimum number of colors in a coloring) equals the size of the maximum clique. According to the weak perfect graph theorem, the complement of
Clique_cover
Graph representing faces of another graph
dual graph. For instance, the four color theorem (the existence of a 4-coloring for every planar graph) can be expressed equivalently as stating that the
Dual_graph
Chemical compound
broad claims that food coloring causes food intolerance and ADHD-like behavior in children. It is possible that certain food coloring may act as a trigger
Azorubine
talking to Donna, Alex mentions how good Iris looks and would Donna consider coloring her hair. Iris tells Donna that Jack now likes her hair. 118 5 "The Monster"
List of The Donna Reed Show episodes
List_of_The_Donna_Reed_Show_episodes
Self-balancing binary search tree
In computer science, a WAVL tree or weak AVL tree is a self-balancing binary search tree. WAVL trees are named after AVL trees, another type of balanced
WAVL_tree
All even-degree subgraphs of a graph
dual graph, a minimum weight basis for its cut space. In planar graphs, colorings with k {\displaystyle k} distinct colors are dual to nowhere-zero flows
Cycle_space
Mathematical problem
thereafter. Chvátal's proof was later simplified by Steve Fisk, via a 3-coloring argument. Chvátal has a more geometrical approach, whereas Fisk uses well-known
Art_gallery_problem
Perception caused by wavelengths of light
systems such as projectors, televisions, and computer terminals. Subtractive coloring uses dyes, inks, pigments, or filters to absorb some wavelengths of light
Color
Red food dye from beets
of amaranth.[citation needed] The most common uses of betanins are in coloring ice cream and powdered soft drink beverages; other uses are in some sugar
Betanin
Plant used as spice
into a deep orange-yellow shelf-stable spice powder commonly used as a coloring and flavoring agent in many Asian cuisines, especially for curries (curry
Turmeric
Chemical compound
organic or reactive compounds. It is typically stored with a stabilizer in a weakly acidic solution in an opaque bottle. Hydrogen peroxide is found in biological
Hydrogen_peroxide
Theory in historical linguistics
Latin sedēmus). It is attested in Celtic, Italic, Germanic (the Class IV weak verbs), and Balto-Slavic, with some traces in Indo-Iranian (In Avestan the
Laryngeal_theory
Property in knot theory
granny knot is tricolorable. In this coloring the three strands at every crossing have three different colors. Coloring one but not both of the trefoil knots
Tricolorability
Chemical compound used as colorant
possible that certain food colorings may act as a trigger in those who are genetically predisposed, but the evidence is weak. "European Parliament and
Sunset_yellow_FCF
Statement in mathematical combinatorics
^{2}\to \{1,2,\dots ,k\}} be a k-coloring of the complete graph on N {\displaystyle \mathbb {N} } . It is a stable coloring iff ∀ n ∈ N {\displaystyle \forall
Ramsey's_theorem
no solutions except 11 + 21 = 31. The Erdős–Faber–Lovász conjecture on coloring unions of cliques, proved (for all large n) by Dong Yeap Kang, Tom Kelly
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Graph with sign-labeled edges
notion of signed graph coloring. Where a coloring of a graph is a mapping from the vertex set to the natural numbers, a coloring of a signed graph is a
Signed_graph
"Mixture of water-soluble organic compounds from Quinoline Yellow dye"
broad claims that food coloring causes food intolerance and ADHD-like behavior in children. It is possible that certain food coloring may act as a trigger
Quinoline_Yellow_WS
Extension of ideas in combinatorics to infinite sets
applying the coloring of Sierpiński to it, we get that ℵ 1 ↛ ( ℵ 1 ) 2 2 {\displaystyle \aleph _{1}\not \rightarrow (\aleph _{1})_{2}^{2}} . Colorings such as
Infinitary_combinatorics
Generalization of graph theory
represented by contiguous subsets of these regions, which may be indicated by coloring, by drawing outlines around them, or both. An order-n Venn diagram, for
Hypergraph
Phylum of photosynthesising prokaryotes
potential applications in biotechnology for bioethanol production, food colorings, as a source of human and animal food, dietary supplements and raw materials
Cyanobacteria
Soft drink
acacia, stabiliser Extract of quillaia, a foaming agent Carmine, food coloring agent (in this example, raspberry flavor) The effervescence, when the powder
Creamola_Foam
Discrete mathematics decomposition
but by the method with the Book embeddings we use a four coloring instead of a binary coloring to get two different Book embeddings, which yields to a
Rectangulations
Russian-American mathematician
Rabern, Landon (2012). "Coloring a graph with Δ−1 colors: Conjectures equivalent to the Borodin–Kostochka conjecture that appear weaker". arXiv:1203.5380 [math
Alexandr_Kostochka
Branch of petrology focusing on detailed descriptions of rocks
dissolved, leaving a film of gelatinous silica that can be stained with coloring matters, such as the aniline dyes (nepheline, analcite, zeolites, etc.)
Petrography
Language spoken by the Lenape people
coloring, etc. A list of processes unique to Unami follow. These are written in linguistic notation. Thus, {ə,a} → ∅ / _{h, x}V when {ə,a} are weak means
Unami_language
Type of crystallographic defect
was radiated with x-rays. A similar result to x-rays was accomplished by coloring the crystals with metal vapors. The photoelectric effect mainly happened
F-center
Species of pear tree
year they may get frozen off before coloring. In the South, Callery pears tend to be among the more reliable coloring trees.[citation needed] A famous example
Pyrus_calleryana
Solid remains of fruit after pressing
tannin-rich.[scientific citation needed] Oenocyanin, a natural red dye and food-coloring agent, is produced from grape pomace.[scientific citation needed] Tartrates
Pomace
Homemade toy
polyvinyl alcohol. Weak hydrogen bonds hold the polymer chains together, while borate molecules link them side by side. These weak bonds give slime its
Slime_(homemade_toy)
Sweetened non-alcoholic drink, often carbonated
or some combination of these. Soft drinks may also contain caffeine, colorings, preservatives and other ingredients. Soft drinks are called "soft" in
Soft_drink
the hair of unwanted deposited color.[citation needed] Most modern hair coloring relies on oxidative reactions. Despite changes in commercial formulations
Hair_dye_stripping
Graph where all long cycles have a chord
several problems that are hard on other classes of graphs such as graph coloring may be solved in polynomial time when the input is chordal. The treewidth
Chordal_graph
Relation between graph coloring and crossings
it as a conjecture in 2007; it is one of his many conjectures in graph coloring theory. The conjecture states that, among all graphs requiring n {\displaystyle
Albertson_conjecture
Fictional character from My Little Pony
a lot because his design is already pretty intimidating! We suggested coloring his upper body black, which helped tone down the intensity and had the
Lord_Tirek
Elimination diet initially devised by Benjamin Feingold
was originally based on the elimination of salicylate, artificial food coloring, and artificial flavors; later on in the 1970s, the preservatives BHA,
Feingold_diet
20th-century consciously learned American accent
postvocalic /r/ is typically dropped. The vowels /ə/ or /ɜː/ do not undergo R-coloring. Linking R is used, but Skinner openly disapproved of intrusive R. In Mid-Atlantic
Good_American_Speech
宀 10 S superintend サイ sai 700 栽 木 10 S plantation サイ sai 701 彩 彡 11 S coloring サイ、いろど-る sai, irodo-ru 702 採 手 11 5 pick サイ、と-る sai, to-ru 703 済 濟 水 11
List_of_jōyō_kanji
Field in logic and theoretical computer science
{\displaystyle G=(V,E)} , if there exists a 3-coloring, then this can be proven by simply giving the coloring. Thus, the proof of 3-colorability has length
Proof_complexity
Metal treatment process
alloys are anodized to increase corrosion resistance and to allow dyeing (coloring), improved lubrication, or improved adhesion. However, anodizing does not
Anodizing
Comic strip by Charles M. Schulz
through nearly 50 years, with no assistants, including the lettering and coloring process. Peanuts was originally sold under the title of Li'l Folks, but
Peanuts
Russian transport van
the launch of the UAZ-450. Cars of this edition have a two-tone retro coloring and stickers in the form of early UAZ emblem (Germany) Rear view of "Jubilee"
UAZ-452
Species of insect producing the crimson dye carmine
lipstick (E120 or Natural Red 4). Carmine dye was used in the Americas for coloring fabrics and became an important export good in the 16th century during
Cochineal
Marvel Comics superhero
film Spider-Man has appeared in comics, cartoons, films, video games, coloring books, novels, records, children's books, and theme park rides. On television
Spider-Man
Dietary supplement
people with Alzheimer's disease. It contains a mixture of water, food coloring, artificial flavors, sugar, docosahexaenoic acid, eicosapentaenoic acid
Souvenaid
Species of shrub
and 6 cm and they grow asymmetrically. They are bell-shaped and their coloring is dark red with a white background. The capsule is globular and contains
Ruizia_boutoniana
Edge-colored graph matching where all edges have distinct colors
exists not only for a proper edge-coloring, but for any coloring in which each color appears on exactly n edges. Some weaker versions of these conjectures
Rainbow_matching
Photographic film type
Pathéchrome in 1929, became one of the most accurate and reliable stencil coloring systems. It incorporated an original print of a film with sections cut
Color_motion_picture_film
Perfect graphs have neither odd holes nor odd antiholes
the size of the maximum clique equals the minimum number of colors in a coloring of the graph; perfect graphs include many well-known graph classes including
Strong_perfect_graph_theorem
October–December Catshead England <1700 Sharp flavor. Lumpy shape and electric green coloring. Width and height 86 mm (3.4 in). Stalk short. Cells ovate, abaxile. Known
List_of_apple_cultivars_(A–K)
Maritime service branch of the Chinese People's Liberation Army
blue/littoral camouflage uniform as standard (now being replaced by more subdued coloring based on the xingkong pattern). The marines are also equipped with amphibious
People's_Liberation_Army_Navy
requirement that each color class be a clique or independent is weaker than the requirement for coloring (in which each color class must be an independent set)
Cocoloring
Antimalarial medication
vision difficulties, diminished reflexes, emotional changes, excessive coloring of the skin, hearing loss, hives, itching, liver problems or liver failure
Hydroxychloroquine
Branch of the Afroasiatic languages
can be distinguished in Akkadian from the zero reflexes of *ḥ, *ʕ by e-coloring adjacent *a, e.g. pS *ˈbaʕal-um 'owner, lord' > Akk. bēlu(m). Hebrew and
Semitic_languages
Marvel Comics character
"used Ann-Margret from the movie Bye Bye Birdie as a guide, using her coloring, the shape of her face, her red hair and her form-fitting short skirts"
Mary_Jane_Watson
2016 Marvel Studios film
little more grounded and a little more hard-core contemporary." That was "coloring our choices a lot" with Parker. On the Spider-Man suit, Joe Russo described
Captain_America:_Civil_War
Tropical evergreen tree with edible fruit
mangosteen peels is traditionally used in Indonesia as natural dye for coloring tenun ikat and batik textiles in brown, dark brown, purple or red hues
Mangosteen
Awareness of internal and external existence
versus seeing other animals. The classic example involves placing a spot of coloring on the skin or fur near the individual's forehead and seeing if they attempt
Consciousness
Chemical compound
I. 42051, is a sky blue synthetic triphenylmethane dye used as a food coloring. As a food additive, it has E number E131. It is a sodium or calcium salt
Patent_Blue_V
conjecture relating coloring to clique minors The Hadwiger–Nelson problem on the chromatic number of unit distance graphs Jaeger's Petersen-coloring conjecture:
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Chemical element with atomic number 79 (Au)
needed] Gold and its salts produce a deep, intense red color when used as a coloring agent in cranberry glass. In photography, gold toners are used to shift
Gold
Ideals in a Boolean algebra can be extended to prime ideals
prime ideal theorem, for instance—represent a property that is strictly weaker than AC. It is due to this intermediate status between ZF and ZF + AC (ZFC)
Boolean_prime_ideal_theorem
Branch of the Chinese language family
more vowel mergers than many other varieties of Mandarin. For example: R-coloring, a characteristic feature of Mandarin, works quite differently in the southwest
Mandarin_Chinese
of coloring have been studied, including edge coloring (coloring edges so that no two edges with the same endpoint share a color), list coloring (proper
Glossary_of_graph_theory
1971 studio album by Pink Floyd
"Echoes" showed Pink Floyd to be a more developed group than before, "coloring the slow guitar ripples with deep-in-the-studio sonic details that only
Meddle
Signal format for standard-definition video
video signal. C is the chroma signal, which carries the chrominance – or coloring-in – of the picture. This signal contains two color-difference components
S-Video
Techniques and therapies to manage stress
simpler activities such as coloring can also be highly effective in reducing stress levels. Coloring therapy, or different coloring activities, offer a creative
Stress_management
External genitalia of the female mammal
the labia minora. In pregnancy, the vulva and vagina take on a bluish coloring due to venous congestion. This appears between the eighth and twelfth week
Vulva
Species of bird
color. Although little regional variation is known in the plumage, adult coloring in the Pacific Northwest averages slightly darker overall. Aberrant pale
Cooper's_hawk
Correlation inequality
amount of blackness), while the second is decreasing. In fact, in any coloring of the hex board exactly one of these two events happen — this is why hex
FKG_inequality
Uranium with lower content of 235U
systems can be affected by exposure to uranium, a toxic metal. It is only weakly radioactive because of the long radioactive half-life of 238U (4.468 billion
Depleted_uranium
Largest species of deer
more aggressive individuals are always darker in color, with the darkest coloring usually in areas facing the opponent, thus serving as a natural warning
Moose
Plastics that reduce static electricity
isolated enough, so that any discharge that happens across the material is weak enough. Electronics portal Antistatic device Electrostatic discharge Electrical
Electrostatic discharge materials
Electrostatic_discharge_materials
American daytime television soap opera (since 1965)
1993 version of the sequence, this variant featured slight changes in the coloring of the sky backdrop. The hourglass sequence was also used during the show's
Days_of_Our_Lives
Horror comic book series
that the work did not live up to its premise's potential despite good coloring and artwork. In contrast, IGN praised Nailbiter #1, stating that it was
Nailbiter_(comic)
Medium-sized mammal native to North America
around the eyes, which contrasts sharply with the surrounding white face coloring. This is reminiscent of a "bandit's mask" and has thus enhanced the animal's
Raccoon
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