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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.
The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators is a book on graph coloring, Ramsey theory, and the history of development of these areas, concentrating in particular on the Hadwiger–Nelson problem and on the biography of Bartel Leendert van der Waerden.
An edge coloring with k colors is called a k-edge-coloring and is equivalent to the problem of partitioning the edge set into k matchings. The smallest number of colors needed for an edge coloring of a graph G is the chromatic index, or edge chromatic number, χ ′ (G). A Tait coloring is a 3-edge coloring of a cubic graph.
According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).
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 ...
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.
This nine-edge Shannon multigraph requires nine colors in any edge coloring; its vertex degree is six and its multiplicity is three. According to a theorem of Shannon (1949) , every multigraph with maximum degree Δ {\displaystyle \Delta } has an edge coloring that uses at most 3 2 Δ {\displaystyle {\frac {3}{2}}\Delta } colors.
This is a list of pages in the scope of Wikipedia:WikiProject Mathematics along with pageviews. ... Graph coloring: 12,702: 423 B: High: 883 Sacred geometry: 12,698: ...
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