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The vertex coloring game was introduced in 1981 by Steven Brams as a map-coloring game [1] [2] and rediscovered ten years after by Bodlaender. [3] Its rules are as follows: Alice and Bob color the vertices of a graph G with a set k of colors. Alice and Bob take turns, coloring properly an uncolored vertex (in the standard version, Alice begins).
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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 ...
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Many 3×3×3 Rubik's Cube enthusiasts use a notation developed by David Singmaster to denote a sequence of moves, referred to as "Singmaster notation" or simple "Cube notation". [58] Its relative nature allows algorithms to be written in such a way that they can be applied regardless of which side is designated the top or how the colours are ...
[3] [4] In the United States, it has been calculated that about one fifth of retail sales [5] to one quarter of all personal spending takes place during the Christmas/holiday shopping season. [6] Figures from the U.S. Census Bureau reveal that expenditure in department stores nationwide rose from $20.8 billion in November 2004 to $31.9 billion ...
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The empty graph E 3 (red) admits a 1-coloring; the complete graph K 3 (blue) admits a 3-coloring; the other graphs admit a 2-coloring. Main article: Chromatic polynomial The chromatic polynomial counts the number of ways a graph can be colored using some of a given number of colors.