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Graph coloring where each vertex has a list of allowed colors
theory, a branch of mathematics, list coloring is a type of graph coloring where each vertex can be restricted to a list of allowed colors. It was first
List_coloring
Graph edge coloring with a limited number of allowed colors
graph coloring that combines list coloring and edge coloring. An instance of a list edge-coloring problem consists of a graph together with a list of allowed
List_edge-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
Cubic graph with 10 vertices and 15 edges
color. It has a list coloring with 3 colors, by Brooks's theorem for list colorings. The Petersen graph has chromatic index 4; coloring the edges requires
Petersen_graph
graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels
Radio_coloring
Theorem in combinatorics
is most naturally expressed in the language of list coloring. For a graph G {\displaystyle G} , a list assignment L {\displaystyle L} attaches to every
Dinitz_theorem
Substance used to color food or drink
Food coloring, color additive or colorant is any dye, pigment, or substance that imparts color when it is added to food or beverages. Colorants can be
Food_coloring
Graph coloring of both the edges and vertices
theory, total coloring is a type of graph coloring on the vertices and edges of a graph. When used without any qualification, a total coloring is always assumed
Total_coloring
2016 mixtape by Chance the Rapper
Coloring Book is the third mixtape by American rapper Chance the Rapper. It was produced by his group The Social Experiment, Lido, and Kaytranada, among
Coloring_Book_(mixtape)
German mathematician
list coloring, and a counterexample to a related conjecture that list coloring of planar graphs requires at most one more color than graph coloring for
Margit_Voigt
On graph coloring and neighborhood size
of it in 1941. A coloring with the number of colors described by Brooks' theorem is sometimes called a Brooks coloring or a Δ-coloring. For any connected
Brooks'_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
Graph operation
complete graph Kk. A similar construction may be used for list coloring in place of coloring. For k = 3, every k-critical graph (that is, every odd cycle)
Hajós_construction
One-by-one assignment of colors to graph vertices
the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring is a coloring of the vertices of a
Greedy_coloring
Water-soluble food coloring
Caramel color or caramel coloring is a water-soluble food coloring. It is made by heat treatment of carbohydrates (sugars), in general in the presence
Caramel_coloring
Area of discrete mathematics
Total coloring conjecture, also called Behzad's conjecture (unsolved) List coloring conjecture (unsolved) Hadwiger conjecture (graph theory) (unsolved)
Graph_theory
on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints, e.g. proper coloring or list coloring) Hopcroft–Karp
List_of_algorithms
Graph coloring with an allowed number of same-color neighbors
mathematical discipline, coloring refers to an assignment of colours or labels to vertices, edges and faces of a graph. Defective coloring is a variant of proper
Defective_coloring
Problem in graph theory
special case of list coloring, the problem of coloring a graph in which no vertices have been colored, but each vertex has an assigned list of available
Precoloring_extension
Goldberg–Seymour conjecture Graph coloring game Graph two-coloring Harmonious coloring Incidence coloring List coloring List edge-coloring Perfect graph Ramsey's
List_of_graph_theory_topics
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
This is a list of notable mathematical conjectures. The following conjectures remain open. The (incomplete) column "cites" lists the number of results
List_of_conjectures
American rapper (born 1993)
figure in Chicago hip-hop and among independent artists. His third mixtape, Coloring Book (2016), received critical acclaim and became the first streaming-only
Chance_the_Rapper
Graph coloring variant in graph theory
In graph theory, a packing coloring (also called a broadcast coloring) is a type of graph coloring where vertices are assigned colors (represented by
Packing_coloring
Orange-red condiment and food coloring derived from the seeds of the achiote tree
Annatto (/əˈnætoʊ/ or /əˈnɑːtoʊ/) is an orange-red condiment and food coloring derived from the seeds of the achiote tree (Bixa orellana), native to tropical
Annatto
In graph theory, circular coloring is a kind of coloring that may be viewed as a refinement of the usual graph coloring. The circular chromatic number
Circular_coloring
Unproven generalization of the four-color theorem
equivalently be stated in the following form. According to it, if all proper colorings of an undirected graph G {\displaystyle G} use k {\displaystyle k} or
Hadwiger conjecture (graph theory)
Hadwiger_conjecture_(graph_theory)
A uniform coloring can be specified by listing the different colors with indices around a vertex figure. In addition, an n-uniform coloring is a property
Uniform_coloring
use computer graphics, and the first Studio Ghibli film to use digital coloring; the first animated feature in Japan's history to gross more than 10 billion
List_of_Studio_Ghibli_works
This is a non-exhaustive list of hairstyles, excluding facial hairstyles. Long hairstyles may be considered those which reach beyond the shoulders on women
List_of_hairstyles
Production methods of colored glass
contains. In an extremely pure glass, without impurities such as bubbles, coloring ions, or crystalline and nano-sized phases, all visible light would pass
Glass coloring and color marking
Glass_coloring_and_color_marking
maintain a person's image. This is achieved using a combination of hair coloring, haircutting, and hair texturing techniques. Most hairdressers are professionally
List_of_hairdressers
Russian-American mathematician
Institute of Mathematics in Novosibirsk, Russia. His research concerns graph coloring, graph minors, extremal graph theory, and hypergraphs. He is known for
Alexandr_Kostochka
This is a list of episodes for the television sitcom The Joey Bishop Show, which was broadcast on NBC for three seasons and then moved to CBS for its fourth
List of The Joey Bishop Show episodes
List_of_The_Joey_Bishop_Show_episodes
2007 studio album by Blockhead
Uncle Tony's Coloring Book is the third solo studio album by American hip hop producer Blockhead. It was released on August 14, 2007. The vinyl edition
Uncle_Tony's_Coloring_Book
and items that are related to Mercer Mayer and his creations (such as coloring books, sticker books, lacing cards and toys). Little Critter is an anthropomorphic
Mercer_Mayer_bibliography
Cat with a three-colored coat
as the state cat because their white, black, and orange coloring is in harmony with the coloring of the Baltimore oriole (the state bird) and the Baltimore
Calico_cat
Graph without four-vertex star subgraphs
maximum degree. A generalization of the edge list coloring conjecture states that, for claw-free graphs, the list chromatic number equals the chromatic number;
Claw-free_graph
Chemical compound
4997. PMID 23644932.{{cite journal}}: CS1 maint: numeric names: authors list (link) Pinazo-Durán, M. D.; Gómez-Ulla, F; Arias, L; et al. (2014). "Do Nutritional
Zeaxanthin
This is a list of Malaysian drinks. The most common and popular Malaysian drinks and beverages are teh (teh tarik) and kopi Tarik (coffee). Teh tarik -
List_of_Malaysian_drinks
American actor and comedian (1951–2014)
to critic James Poniewozik. Mork became popular, featured on posters, coloring books, lunch-boxes, and other merchandise. Mork & Mindy was such a success
Robin_Williams
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
electricity, and lightning. Additionally tying Jamie to Shango are the red coloring of his powers, with red being a color often associated with Shango, their
List of characters in mythology novels by Rick Riordan
List_of_characters_in_mythology_novels_by_Rick_Riordan
Process of changing the color of metal surfaces with different chemical solutions
The chemical coloring of metals involve processes that change the color of metal surfaces with different chemical solutions. These processes can be categorized
Chemical_coloring_of_metals
American film director (born 1981)
In 2021, frequent collaborator Chance the Rapper released Magnificent Coloring World, a concert film made from special performance footage Schreier directed
Jake_Schreier
cavies with other than separately recognized combinations of colors, the coloring is described in order of magnitude (i.e., a mostly lilac cavy with some
List_of_guinea_pig_breeds
Rokenbok Stickle bricks STIKFAS Tinkertoy Tog'l Zaks Zome Cleversticks Coloring book Colorforms Crayola Crayons Creepy Crawlers Lego Lite-Brite Magic Slate
List_of_toys
Every triangle-free planar graph is 3-colorable
girth at least five is 3-list-colorable. However, Grötzsch's theorem itself does not extend from coloring to list coloring: there exist triangle-free
Grötzsch's_theorem
following table – with FMA4 instructions highlighted with * and yellow cell coloring, and FMA3 instructions not highlighted: Vector register lanes are counted
List_of_x86_SIMD_instructions
are currently 616 games on this list. List of video games based on comics List of video games based on cartoons List of video games based on anime or
List of video games based on films
List_of_video_games_based_on_films
vertex. These 11 uniform tilings have 32 different uniform colorings. A uniform coloring allows identical sided polygons at a vertex to be colored differently
List of Euclidean uniform tilings
List_of_Euclidean_uniform_tilings
Iodo-derivative of fluorone used as a pink dye
It is a red-pink dye used for food coloring, cosmetics, hair coloring, pet products, and diverse industrial colorings. It is the disodium salt of 2,4,5
Erythrosine
provided much needed medical aid to her folk. She appears to have similar coloring as her daughters but is always hidden in a full-length, hooded robe. Vurdah
List_of_Elfquest_characters
representation in video games. The Electronic Gaming Monthly staff found her pink coloring and tendency to run from danger to be stereotypical and common in Japanese-created
List of Sonic the Hedgehog characters
List_of_Sonic_the_Hedgehog_characters
cuisine List of baked goods List of bread rolls List of breads List of buns List of cakes List of choux pastry dishes List of desserts List of doughnut
List_of_pastries
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
Soviet Ukrainian mathematician (1937–2017)
to graph theory and graph coloring, including the introduction of list coloring,[V76] the formulation of the total coloring conjecture (still unsolved)
Vadim_G._Vizing
American writer (born 1979)
which became the publisher's most-preordered book of all time. A planned coloring book for It Ends with Us was canceled in January 2023 following online
Colleen_Hoover
A list of avant-garde and experimental films made in the 1930s. Unless where noted, all films had sound and were in black and white. Jan Christopher Horak
List of avant-garde films of the 1930s
List_of_avant-garde_films_of_the_1930s
Body hair in the genital region
Volumizer Wax Hair texture powder Haircare techniques Backcombing Hair coloring Crimping Curly Girl Method Hair cutting Hair highlighting Perm Shampoo
Pubic_hair
caffeine, colorings, preservatives and other ingredients. Craft soda List of brand name soft drink products List of soft drink flavors List of soft drink
List_of_drinks
Algorithms and methods of plotting the Mandelbrot set on a computing device
show structures of the data (scientific visualisation) A more complex coloring method involves using a histogram which pairs each pixel with said pixel's
Plotting algorithms for the Mandelbrot set
Plotting_algorithms_for_the_Mandelbrot_set
Chemical compound
range of applications, including paint, sunscreen, and food coloring. When used as a food coloring, it has E number E171. World production in 2014 exceeded
Titanium_dioxide
Unsolved problem on graph coloring
problem is an unsolved problem on graph coloring in mathematics. It is an extension of the planar map coloring problem (solved by the four color theorem)
Earth–Moon_problem
harmful. Examples include restricting food consumption to foods without colorings or preservatives, taking supplements, or drinking large amounts of water
List_of_diets
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
Hermes Press also publishes original content such as Scratch9. This is a list of Hermes Press publications. Contents 0–9 A B C D E F G H I J K L M N O
List of Hermes Press publications
List_of_Hermes_Press_publications
Tanner's portrait of his wife, Head of a Girl in Jerusalem. The gold-orange coloring and characterful expression point to Tanner's mature work. Mosby, Dewey
List of paintings by Henry Ossawa Tanner
List_of_paintings_by_Henry_Ossawa_Tanner
cycle-continuous mapping to the Petersen graph The list coloring conjecture: for every graph, the list chromatic index equals the chromatic index The overfull
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
century in a book about making colorants, where the lacca is used as a coloring ingredient – namely this is the book Compositiones Variae, which survives
List of English words of Arabic origin (K–M)
List_of_English_words_of_Arabic_origin_(K–M)
Bucerotiformes Family: Upupidae Hoopoes have black, white and orangey-pink coloring with a large erectile crest on their head. Common hoopoe (hærfugl), Upupa
List_of_birds_of_Norway
American mathematician (born 1956)
Inductions in Reasonable Structures. In 1979, Rubin co-authored a paper on list coloring of graphs with Paul Erdős, giving him an Erdős number of 1. Rubin, A
Arthur_Rubin
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
the vast majority are not suitable for mass production. In the following list, use for "eating" means that the fruit is consumed raw, rather than cooked
List_of_apple_cultivars_(A–K)
Food portal Lists portal List of baked goods List of breads List of buns List of desserts List of pancakes List of pastries List of pies, tarts and flans
List_of_cakes
Independent set in a graph
rainbow-independent set in its complement graph. Graph coloring List coloring Rainbow coloring Rainbow-colorable hypergraph Independence complex Aharoni
Rainbow-independent_set
American comic book colorist
the greatest colorists of all time. She won the Eisner Award for Best Coloring five times, in 2014, 2016, 2023, 2024, and 2025, and has amassed the second
Jordie_Bellaire
American fantasy drama TV series (2011–2019)
actors, such as Jack Gleeson and Sophie Turner, received frequent hair coloring. For characters such as Daenerys (Clarke) and her Dothraki, their hair
Game_of_Thrones
Places: Weekly List Actions", retrieved August 7, 2026. Numbers represent an alphabetical ordering by significant words. Various colorings, defined here
National Register of Historic Places listings in the Marshall Islands
National_Register_of_Historic_Places_listings_in_the_Marshall_Islands
that requires four colors in any proper edge coloring. The smallest snark is the Petersen graph, already listed above. Blanuša snark (first) Blanuša snark
List_of_graphs
acesulfame-K, aspartame and cyclamate. Soft drinks may also contain caffeine, colorings, preservatives and other ingredients. Almond – common mixed flavor in
List_of_soft_drink_flavors
threat" to Israel. Israeli Police confiscated books, including children's coloring book titled "From the river to the sea", and arrested the owner of two
Timeline of the Gaza war (19 January 2025 – 17 March 2025)
Timeline_of_the_Gaza_war_(19_January_2025_–_17_March_2025)
2011 EP by Glassjaw
Coloring Book is the fourth extended play by the American post-hardcore band Glassjaw, self-released on February 13, 2011. The release was initially exclusively
Coloring_Book_(Glassjaw_EP)
hurt his best friend. As Gai utilizes dark Soma (marked by a dark blue coloring instead of the normal golden), Shurato eventually realizes Gai is under
List of Legend of Heavenly Sphere Shurato characters
List_of_Legend_of_Heavenly_Sphere_Shurato_characters
Wild cat species native to the Americas
approximately 50 kg (110 lb), about the same as female cougars. Cougar coloring is plain tawny, ranging from silvery-grey to reddish with lighter patches
Cougar
sophisticated vocal capabilities of the songbirds. Most, but not all, have plain coloring. Black-crowned tityra, Tityra inquisitor Black-tailed tityra, Tityra cayana
List_of_birds_of_Argentina
German multinational pharmaceutical and biotechnology company
Zitzlsperger 2016, p. 92. Fagin D. "Dye Me a River: How a Revolutionary Textile Coloring Compound Tainted a Waterway [Excerpt]". Scientific American. Retrieved
Bayer
This is the list of episodes of The Late Show with Stephen Colbert that aired in 2015. Pedersen, Erik (September 8, 2015). "Stephen Colbert's 'Late Show'
List of The Late Show with Stephen Colbert episodes (2015)
List_of_The_Late_Show_with_Stephen_Colbert_episodes_(2015)
Animation technique in which frames are hand-drawn
animation List of animated feature-length films List of animated short series List of animated television series List of animation studios List of years
Traditional_animation
American singer (born 1984)
"I know exactly the record I want to make next. I know the artwork, the coloring and the tone" and "I even know what type of tour I'm doing next. I'll be
Katy_Perry
diary is the Hyper Vision Diary (はいぱーびじょんだいありー, Haipā Bijon Daiarī), a coloring book that gives a small summary of the activities that he may perform for
List of Future Diary characters
List_of_Future_Diary_characters
Russian singer-songwriter (born 1998)
places, respectively, in their list of the 50 best tracks of 2018, and according to the results of a popular vote, Coloring for Adults came third among the
Monetochka
give a child a realistic palette for coloring their world." The eight colors used came from their standard list of colors (none of these colors are exclusive
List_of_Crayola_crayon_colors
also contain caffeine, colorings, preservatives and other ingredients. Soft drinks that are sold in more than one country are listed in this article only
List of soft drinks by country
List_of_soft_drinks_by_country
pandemic. Productions which heavily rely on outsourcing in-between and coloring work to studios in China were the most affected by the COVID-19 pandemic
Impact of the COVID-19 pandemic on television
Impact_of_the_COVID-19_pandemic_on_television
Chemical compound
the E number E161a as a food coloring although it is not approved for use in the EU or USA.[citation needed] It is listed as food additive 161a in Australia
Flavoxanthin
December 2019. Monterey Jack is a stirred curd Cheddar without any annatto coloring. It is sweeter than most and milder when young. "Muenster Cheese - AnyCheese"
List_of_cheeses
sophisticated vocal capabilities of the songbirds. Most, but not all, have plain coloring. Nine species have been recorded in Paraguay. Black-crowned tityra, Tityra
List_of_birds_of_Paraguay
American hip-hop trio from New Jersey
greatest rap groups, VH1 ranked them 17th on its 50 Greatest Hip-Hop Artists list. The Score appears on Rolling Stone's 500 Greatest Albums, while "Ready or
Fugees
The following is a list of episodes of the television series The Tonight Show Starring Johnny Carson which aired in 1980:[citation needed] Liebenson, Donald
List of The Tonight Show Starring Johnny Carson episodes (1980)
List_of_The_Tonight_Show_Starring_Johnny_Carson_episodes_(1980)
LIST COLORING
LIST COLORING
Surname or Lastname
English (East Anglia)
English (East Anglia) : metonymic occupational name for a cobbler, or perhaps a metonymic occupational name for a maker of cobblers’ lasts (see Laster).German and Jewish (Ashkenazic) : metonymic occupational name for a porter, from Middle High German last; German Last or Yiddish last ‘burden’, ‘load’.Dutch : metonymic occupational name as in 2, from Middle Dutch last ‘load’, ‘burden’; or a nickname for an awkward character, from Dutch last ‘trouble’, ‘nuisance’.French : habitational name from a place so named in Puy-de-Dôme.
Boy/Male
Anglo Saxon
Cunning.
Female
French
French form of German Elise, ÉLISE means "God is my oath."Â
Girl/Female
Danish American German Hebrew Greek French
Male
Native American
Native American Miwok name LISE means "salmon head rising above water." Compare with feminine Lise.
Girl/Female
German American Hebrew Greek English
Devoted to God.
Female
Italian
 Short form of Italian Elisabetta, LISA means "God is my oath." Compare with another form of Lisa.
Surname or Lastname
English
English : metonymic occupational name for a dresser of flax, from Middle English lynet, lynt ‘flax’.Dutch : from a short form of a Germanic name formed with lind (see Linde 1).Dutch : metonymic occupational name for a linen weaver or merchant.
Surname or Lastname
English and Scottish
English and Scottish : unexplained. The name has been recorded in Glastonbury, Somerset, since 1705.Perhaps a variant of Czech LiÅ¡ka, (see Liska), Slovak LÃÅ¡ka, or German Liske.
Female
English
Short form of English Elisabeth, LIS means "God is my oath."Â
Boy/Male
Native American
Salmon's head rising above water.
Girl/Female
Australian, Danish, Swedish
God's Promise; God is My Oath
Girl/Female
Australian, Danish, Swedish
God's Promise; God is My Oath
Surname or Lastname
Jewish
Jewish : shortened form of some Ashkenazic surname such as Littman or Litwin.English : variant of Light ‘little’.Dutch and North German : from a short form of a Germanic personal name formed with liut ‘people’, ‘tribe’ as the first element.
Male
Hungarian
Hungarian form of Latin Valentinus, BÃLINT means "healthy, strong."
Surname or Lastname
English (Devon and Cornwall)
English (Devon and Cornwall) : probably a variant spelling of Guest.
Surname or Lastname
English and Scottish
English and Scottish : unexplained. Probably a shortened form of northern Irish and Scottish McLeish.
Female
Norwegian
Danish and Norwegian form of German Liese, LISE means "God is my oath."Â Compare with masculine Lise.
Female
English
 Variant spelling of English Liza, LISA means "God is my oath." Compare with another form of Lisa.
Female
Hebrew
(לִי×ַתּ) Hebrew name LIAT means "you are mine."
LIST COLORING
LIST COLORING
LIST COLORING
LIST COLORING
LIST COLORING
LIST COLORING
LIST COLORING
v. t.
Not employed or enjoyed; thrown away; employed ineffectually; wasted; squandered; as, a lost day; a lost opportunity or benefit.
v. t.
To shape with a last; to fasten or fit to a last; to place smoothly on a last; as, to last a boot.
v. t.
Ruined or destroyed, either physically or morally; past help or hope; as, a ship lost at sea; a woman lost to virtue; a lost soul.
n.
A roll or catalogue, that is row or line; a record of names; as, a list of names, books, articles; a list of ratable estate.
v. t.
To inclose for combat; as, to list a field.
v. i.
To lean; to incline; as, the ship lists to port.
3d pers. sing. pres.
of Last, to endure, contracted from lasteth.
v. t.
Hardened beyond sensibility or recovery; alienated; insensible; as, lost to shame; lost to all sense of honor.
n.
Lust; desire; pleasure.
v. t.
To strike with the fist.
n.
An inclination to one side; as, the ship has a list to starboard.
v. t.
To cut away a narrow strip, as of sapwood, from the edge of; as, to list a board.
a.
Last; least.
v. t.
Parted with; no longer held or possessed; as, a lost limb; lost honor.
v. t.
To gripe with the fist.
v. t.
To enroll; to place or register in a list.
v. t.
To cover with list, or with strips of cloth; to put list on; as, to list a door; to stripe as if with list.
n.
To list; to like.
n.
A lift gate. See Lift gate, below.
v. t.
To pronounce with a lisp.