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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.
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
An edge coloring of a graph is a proper coloring of the edges, meaning an assignment of colors to edges so that no vertex is incident to two edges of the same color. 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.
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 ...
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: ...
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).
The classical map-coloring problem requires that no two neighboring regions be given the same color. The classical move constraint enforces this by prohibiting coloring a region with the same color as one of its neighbor. The anticlassical constraint prohibits coloring a region with a color that differs from the color of one of its neighbors.