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Assignment of colors to graph vertices that destroys all symmetries
and coloring. The minimum number of colors in a distinguishing coloring is called the distinguishing number of the graph. Distinguishing colorings and
Distinguishing_coloring
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
Vertex coloring where no two linked nodes have the same color pairing
(1982). "The line-distinguishing chromatic number of a graph". Ars Combin. 14: 241–252. Jensen, Tommy R.; Toft, Bjarne (1995). Graph coloring problems. New
Harmonious_coloring
Colour convention for differentiating atoms
In chemistry, the CPK coloring (for Corey–Pauling–Koltun) is a popular color convention for distinguishing atoms of different chemical elements in molecular
CPK_coloring
Type of total coloring in graph theory
C(u) ≠ C(v). In graph theory, a total coloring is an adjacent-vertex-distinguishing-total-coloring (AVD-total-coloring) if it has the following additional
Adjacent-vertex-distinguishing-total coloring
Adjacent-vertex-distinguishing-total_coloring
Area of discrete mathematics
Percy John Heawood, Frank P. Ramsey and Hadwiger led to the study of the colorings of the graphs embedded on surfaces with arbitrary genus. Tait's reformulation
Graph_theory
Mapping a graph onto itself without changing edge-vertex connectivity
families are indicated by the following table: Algebraic graph theory Distinguishing coloring Frucht, R. (1938), "Herstellung von Graphen mit vorgegebener abstrakter
Graph_automorphism
Cubic graph with 10 vertices and 15 edges
three colors in any (possibly improper) coloring that breaks all of its symmetries; that is, its distinguishing number is three. Except for the complete
Petersen_graph
American mathematician
of partially ordered sets, and known for her research on proper distinguishing colorings of graphs and on tolerance graphs. She is the Lewis Atterbury Stimson
Ann_Trenk
Heuristic test for graph isomorphism
receive the same coloring, the test is inconclusive. An example of two non-isomorphic graphs the Weisfeiler–Leman test cannot distinguish is given here.
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
Table coloring to improve readability
Zebra striping is the coloring of every other row of a table to improve readability. Especially in wide tables with numerous columns, it can be difficult
Zebra_striping
American breed of horse
Americas club if they have Appaloosa coloring visible from 40 feet (12 m), otherwise known as "loud" Appaloosa coloring. The coloration includes the typical
Pony_of_the_Americas
Breed of domestic cat
of the Cat Fancy (GCCF). It was later renamed Turkish Van to better distinguish it from the Turkish Angora breed. The Turkish Van has been claimed to
Turkish_Van
Dog breed
and straight guard hairs, which appear white but have a hint of silver coloring. This top layer keeps the undercoat relatively clean and free of debris
Samoyed_dog
American mathematician
department. Her research involved the symmetries of graphs and distinguishing colorings of graphs. Boutin was a 1975 graduate of Chicopee Comprehensive
Debra_Boutin
Function in algebraic graph theory
graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George
Chromatic_polynomial
Focusing on what is irrelevant but easy to understand
item, writing: "There may be members of the committee who might fail to distinguish between asbestos and galvanised iron, but every man there knows about
Law_of_triviality
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
Species of fish
however, males may have more intense coloring, particularly in dominant or sexually active males. Another key distinguishing feature of P. cyaneorhabdos from
Pseudotropheus_cyaneorhabdos
1922 Anglo-Turkish war scare
may impede users' ability to distinguish links from regular text, or links colored for purely aesthetic reasons. Coloring also may not appear correctly
Chanak_crisis
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
Species of mammal
similar to the common duiker, it is smaller in size and has a distinguishing reddish coloring. Additionally, the red forest duiker favors a denser bush habitat
Red_forest_duiker
Part of an animal that is behind the loins and below the tail
plumage on the rump is a characteristic widely used by ornithologists to distinguish between related species, and sometimes also between males and females
Rump_(animal)
American mathematician and violinist
undergraduate research, which resulted in three published papers on distinguishing colorings of Cayley graphs. Chan was given a Sloan Research Fellowship in
Melody_Chan
Traditional herbal liqueur or aperitif in the Alpine regions of Europe
Cheaper versions may be made bright green through the addition of food coloring. Because génépi is produced by steeping the aromatic flowering tops of
Génépi
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
Pigment, aluminium salt of carminic acid
Female Dactylopius coccus (cochineal) insects were used for their red coloring power as early as 700 BC. American civilizations (from the American continent)
Carmine
Tool of editors for programming, scripting, and markup
comment at the beginning is also highlighted in a specific manner to distinguish it from working code. The ideas of syntax highlighting overlap significantly
Syntax_highlighting
Geometric graph with unit edge lengths
There exist unit distance graphs requiring five colors in any proper coloring, and all unit distance graphs can be colored with at most seven colors
Unit_distance_graph
Thin slice of a material prepared for microscopic examination
twinning or inclusions in the grain. However, for certainty, other distinguishing features of quartz include the fact that it is uniaxial, it has a positive
Thin_section
Species of butterfly
spots are discontinuous, allowing the blue or green coloring to spread medially. The distinguishing difference in color between the two subspecies is evident
Papilio_troilus
Twenty-second letter of the Latin alphabet
vanadium. It is number 23 on the periodic table. Emerald derives its green coloring from either vanadium or chromium. v, v., and vs can also be used as an
V
Color used in designing web pages
values are also available. Recent W3C specifications of color names distinguish between basic and extended colors. In HTML and XHTML, colors can be used
Web_colors
Edible species of fungus
as the two-colored bolete or red and yellow bolete after its two-tone coloring scheme, is a species of fungus in the genus Baorangia. Its fruit body,
Baorangia_bicolor
Group of plant cultivars
Thick, bamboo-like stems with swollen nodes are the defining features distinguishing them from other types of begonias. Many are free-flowering, with large
Cane_begonia
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
Traditional European nautical symbol
(see Jolly Roger). The origin of bloody flags is unknown, but deep red coloring is strongly associated with the color of blood and thus symbolises suffering
Bloody_flag
Miscegenation history
this, black individuals began intermarrying with people of lighter skin coloring such as blancos (whites) and mestizos. This was done as a means of better
History_of_miscegenation
Species of flowering plant
white that tend to be hinted with pink or red sepals, with red ovaries coloring the center of the flowers, and red anthers that turn golden. The flowers
Crassula_undulata
American manufacturer of building materials
1956. To distinguish its product, the company dyed their insulation pink by adding red dye to the AF wool. However, considering that the coloring made the
Owens_Corning
Frozen dessert
or fruit juice, citric or tartaric acids, flavoring preparation, food coloring, sequestering agent(s), and lactose. Some early 20th-century American recipes
Sherbet_(frozen_dessert)
Southern United States, plus African-American English. Mergers before /r/: R-coloring has led to some vowel mergers before historical /r/ that do not happen
Regional_accents_of_English
Handheld game console
display, introducing color for enhanced visual quality. One of its distinguishing features was its dual-orientation design, allowing gameplay in both
WonderSwan
Phonetic sound in some languages
start, car [ɔ˞]: north, war In words such as start, many speakers have r-coloring only in the coda of the vowel, rather than as a simultaneous articulation
R-colored_vowel
Semi-solid oily spread often used as a butter substitute
coloring of the stark white margarine by 1902. In response, margarine companies distributed margarine together with a packet of yellow food coloring.
Margarine
Breed of horse
combining the refined phenotype of the Arabian with the leopard-spotted coloring of the Appaloosa. As both breeds are noted for endurance and intelligence
AraAppaloosa
Protocol for use with Bitcoin transactions
particular bitcoin, it is possible to distinguish a group of bitcoins from the others, a process known as bitcoin coloring (a term that served as a basis to
Colored_Coins
Genetic pattern in a dog's coat
addition to altering the base coat color, merle also modifies eye color and coloring on the nose and paw pads. The merle allele modifies the dark pigment, resulting
Merle_(dog_coat)
Culture of mocking embarrassing content
a cosplayer filling a hotel bathtub with Sharpies to achieve gray skin coloring (emulating the design of the Homestuck characters). Over the following
Cringe_culture
Species of beetle
mostly black and gray with rusty brown coloring on the femora of their front and middle sets of legs, which distinguishes them from similar species of Mordella
Mordella_hubbsi
Writing material made from animal skins
membrane is sometimes used by libraries and museums that wish to avoid distinguishing between parchment and vellum. Today the term parchment is often used
Parchment
Species of marsupial
reddish-brown and its ventral pelage is grayish. Researchers believe this coloring is product of adaptation to a humid forest environment. Potential predators
Rufous_mouse_opossum
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
Coloring and resistance to corrosion of cars
driven by the progression of technologies and by the desire to both distinguish new technologies and relate to previous technologies for the same purpose
Automotive_paint
Species of insect
yellow or black, making the females dimorphic. The yellow morph has similar coloring to the male, but with a conspicuous band of blue spots along the hindwing;
Papilio_glaucus
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
the rural postman problem. Clique cover problem Clique problem Complete coloring, a.k.a. achromatic number Cycle rank Degree-constrained spanning tree Domatic
List_of_NP-complete_problems
may impede users' ability to distinguish links from regular text, or links colored for purely aesthetic reasons. Coloring also may not appear correctly
Child marriage in the United States
Child_marriage_in_the_United_States
Modification to playing cards
cheat or for magicians to perform magic tricks. To be effective, the distinguishing mark or marks must be visible on the obverse sides of the cards, which
Card_marking
Species of amphibian
both of the aforementioned in physical appearance and habitat. The frogs' coloring ranges from mint-gray to light olive green, and brown spots distribute
Atlantic_Coast_leopard_frog
Breed of horse
is known for its primitive features, including a convex profile and dun coloring with primitive markings. Concerning its origins, a theory has been advanced
Sorraia
Japanese artist (1934–2024)
2015 (reprint), Fukkan dot-com, ISBN 978-4-8354-5196-1 Takahashi Macoto Coloring Book (高橋真琴 ぬりえブック), 2016, Genkōsha, ISBN 978-4-7683-0730-4 Romantic Otome
Macoto_Takahashi
Species of amphibian
with sandy soils. It is nocturnal and spends the day in a burrow. Its coloring is usually brown but can be red, gray, or black. It is approximately 8 cm
Southern_toad
Breed of draft horse from France
work and pulling carriages. Percherons are generally gray or black in coloring. The head has a straight profile, broad forehead, large eyes and long thin
Percheron
Mark made as a proof of identity and intent
form of a signature block, only including one's name, often with some distinguishing prefix, can be used to simply indicate the end of a post or response
Signature
saliva with the makeup and effects teams, using a mild mouthwash and food coloring that he squirted into his mouth before filming. He later commented that
Special effects of Batman Returns
Special_effects_of_Batman_Returns
Species of lizard
thighs, there are 35–57 scales. Many other lizards have similar bright-blue coloring. The eastern fence lizard, S. undulatus, instead of having one large patch
Western_fence_lizard
Species of spider
and 1.54 to 2.25 mm at its narrowest point. The male of this species distinguishes itself from other males of the genus by its coiling embolus. The male's
Agelenopsis_pennsylvanica
Horse coat color
spotting patterns including leopard patterns seen on Appaloosas and the pinto coloring known as piebald. The genetics behind the black horse are relatively simple
Black_horse
Domesticated brown rat subspecies
are significant differences that set them apart: the most apparent is coloring. Random color mutations may occur in the wild, but these are rare. Most
Fancy_rat
Primary color
from the madder plant virtually ceased. The most common synthetic food coloring today is Allura Red AC, a red azo dye that goes by several names including:
Red
Species of beetle
commonly confused with the cigarette beetle, as they have a similar size and coloring. Adults possess antennae ending in 3-segmented clubs, while cigarette beetles
Drugstore_beetle
Species of snake
pronounced towards the tail. This coloring gives B. constrictor subspecies the common name of "red-tailed boas." The coloring works as a very effective camouflage
Boa_constrictor
determining if the cancer is a type that produces mucin. Example would be to distinguish between high grade Mucoepidermoid Carcinoma of the parotid, which stains
Mucicarmine_stain
1994 video game
game offers three difficulty levels over a total of 21 matches. Its distinguishing quality was that each of the characters were composed completely of
Ballz
Hematologic stain that facilitates the visual differentiation of blood cell types
stain, a modification of the Romanowsky stain, in 1902. Because it distinguishes easily between blood cells, it became widely used for performing differential
Wright's_stain
Species of fungus
of the three subgenera he proposed were found to be polyphyletic. The coloring of the fruit bodies is quite variable, ranging from violet to amethyst
Clavaria_zollingeri
Subspecies of bird
the closely related red-lored amazon, with a black beak and more subdued coloring. Lilacine amazons are said to make favorable companion parrots because
Lilacine_amazon
Aesthetic style in personal computers
microcomputers like the Apple II and the IBM Personal Computer, whose neutral coloring was selected to blend inconspicuously into corporate and home environments
Beige_box
Strong, bright, deep reddish purple color
the Royal Canadian Mounted Police. Nowadays carmine dyes are used for coloring foodstuffs, medicines and cosmetics. As a food additive in the European
Crimson
Subspecies of mammal
distinguish in the wild. Southern fox squirrels have a wide variety of color morphs and have been considered to have the widest variety of coloring among
Southern_fox_squirrel
Species of beetle
than the male and has yellow and black elytra coloring rather than the male's white and black coloring. It produces one generation a year. The flight
Neoclytus_caprea
Harvest of grapes in order to produce wine
distinguishing grape clusters from mud, leaves and other particles. Despite the improvement many harvesters still have difficulties in distinguishing
Harvest_(wine)
Species of spider
diurnal, which means it is active during the day. Spiders with less silver coloring are better at catching prey, as the silver is bright and warns their prey
Cyclosa_argenteoalba
Species of fish
extend past the eye, sleek figure, etc.) with one exception; the green coloring tends to extend lower on the body past the lateral line than their relatives
Guadalupe_bass
American cigarette brand
company claimed the change was made because the copper used in the green coloring was needed for World War II, though, in reality, American Tobacco used
Lucky_Strike
R-coloring in Mandarin Chinese syllables
"rhotacization of syllable finals", is a phonological process that adds r-coloring or the er (儿; 兒 [ɚ]) sound to syllables in spoken Mandarin Chinese. Erhuayin
Erhua
Metaethical position that some actions are intrinsically right or wrong
Rorschach inkblot tests, also his namesake, with the mask's black and white coloring never touching each other, and therefore consistent with his sense and
Moral_absolutism
Dog breed
needed] and, most importantly, short-coated dog, potentially as a way to distinguish it from the Pekingese, which was of similar build. Many people today
Pug
Hair coat color of horses
that creates black base coat. While the basic genetics that create bay coloring are fairly simple, the genes themselves and the mechanisms that cause shade
Bay_(horse)
triangles, the small cubicuboctahedron can be interpreted as a non-regular coloring of the combinatorially regular (not just uniform) tiling of the genus 3
Small_cubicuboctahedron
Species of edible plant
be obtained. Purple sweet potato color is also used as a natural food coloring. Cuttings of sweet potato vine, either edible or ornamental cultivars,
Sweet_potato
Japanese manga series by Hirohiko Araki
shading techniques in Western art, and classical paintings; the manga coloring is based on calculations rather than consistency, with Araki citing artists
JoJo's_Bizarre_Adventure
the work of Errera, these counterexamples did not show that the whole coloring algorithm fails. Rather, they assumed that all but one vertex of the graph
Errera_graph
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
Population of Giraffe
distinguishable from other subspecies. The most obvious sign is in the coloring of the coat or pelt. Whereas the reticulated giraffe has very clearly defined
Rothschild's_giraffe
Eyesight capabilities of horses
American Paint Horse is a breed wherein most representatives are of pinto coloring "Cream dilution (CrD." Australian Equine Genetics Research Centre, web
Equine_vision
Dolls popular in the early 20th century
and other memorabilia, such as dishware, rattles, soap, pepper shakers, coloring books, poetry collections, and stationery. O'Neill also famously used the
Kewpie
Species of bird
colour of the fulvescens phenotype is usually contrasted with diffuse dark coloring around the eyes, on the leading edges of wings, and more rarely and sparsely
Greater_spotted_eagle
Scottish philosopher, historian, economist and essayist (1711–1776)
moderation, but ... it was moderation with an anti-Whig, pro-royalist coloring." For "Hume shared the ... Tory belief that the Stuarts were no more high-handed
David_Hume
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DISTINGUISHING COLORING
DISTINGUISHING COLORING
DISTINGUISHING COLORING
DISTINGUISHING COLORING
DISTINGUISHING COLORING
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DISTINGUISHING COLORING
DISTINGUISHING COLORING
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