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5:2-coloring of Dodecahedral graph. A 4:2-coloring of this graph does not exist. Fractional coloring is a topic in a young branch of graph theory known as fractional graph theory. It is a generalization of ordinary graph coloring. In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices — those ...
Complete coloring; Edge coloring; Exact coloring; Four color theorem; Fractional coloring; Goldberg–Seymour conjecture; Graph coloring game; Graph two-coloring; Harmonious coloring; Incidence coloring; List coloring; List edge-coloring; Perfect graph; Ramsey's theorem; Sperner's lemma; Strong coloring; Subcoloring; Tait's conjecture; Total ...
Coloring or colouring may refer to: Color, or the act of changing the color of an object Coloring, the act of adding color to the pages of a coloring book; Coloring, the act of adding color to comic book pages, where the person's job title is Colorist; Graph coloring, in mathematics; Hair coloring; Food coloring; Hand-colouring of photographs ...
The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5 .
Bodlaender & Fomin (2005) showed that, given a graph G and a number c of colors, it is possible to test whether G admits an equitable c-coloring in time O(n O(t)), where t is the treewidth of G; in particular, equitable coloring may be solved optimally in polynomial time for trees (previously known due to Chen & Lih 1994) and outerplanar graphs.
An incidence coloring of a graph is an assignment of a color to each incidence of G in such a way that adjacent incidences get distinct colors. It is equivalent to a strong edge coloring of the graph obtained by subdivising each edge of G {\displaystyle G} once.
Precoloring extension may be seen as a 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 colors. To transform a precoloring extension problem into a list coloring problem, assign each uncolored vertex in the precoloring extension problem a ...
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