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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 above shows that in terms of the number of vertices, the upper bound () is the best possible in general. In fact, a rainbow coloring using colors can be constructed by coloring the edges of a spanning tree of in distinct colors. The remaining uncolored edges are colored arbitrarily, without introducing new colors.
With four colors, it can be colored in 24 + 4 × 12 = 72 ways: using all four colors, there are 4! = 24 valid colorings (every assignment of four colors to any 4-vertex graph is a proper coloring); and for every choice of three of the four colors, there are 12 valid 3-colorings. So, for the graph in the example, a table of the number of valid ...
To use a colour in a template or table you can use the hex triplet (e.g. #CD7F32 is bronze) or HTML color name (e.g. red).. Editors are encouraged to make use of tools, such as Color Brewer 2 to create Brewer palettes, listed at MOS:COLOR for color scheme selection used in graphical charts, maps, tables, and webpages with accessibility in mind for color-blind and visually impaired users.
The graphs that are both perfect graphs and -perfect graphs are exactly the chordal graphs. On even-hole-free graphs more generally, the degeneracy ordering approximates the optimal coloring to within at most twice the optimal number of colors; that is, its approximation ratio is 2. [20]
Eight asymmetric graphs, each given a distinguishing coloring with only one color (red) A graph has distinguishing number one if and only if it is asymmetric. [3] For instance, the Frucht graph has a distinguishing coloring with only one color. In a complete graph, the only distinguishing colorings assign a different color to each vertex. For ...
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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.