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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.
(Optional) Color in hex format used for background behind the name of the color. Defaults to value specified by the hex parameter. caption (Optional) Appears under image, if specified. caveat (Optional) Additional text to display at the bottom of the infobox. colorspace (Optional) Colorspace of this color. image (Optional) Name of an image to ...
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 ...
A parsimonious coloring, for a given graph and vertex ordering, has been defined to be a coloring produced by a greedy algorithm that colors the vertices in the given order, and only introduces a new color when all previous colors are adjacent to the given vertex, but can choose which color to use (instead of always choosing the smallest) when ...
Box-drawing characters, also known as line-drawing characters, are a form of semigraphics widely used in text user interfaces to draw various geometric frames and boxes. These characters are characterized by being designed to be connected horizontally and/or vertically with adjacent characters, which requires proper alignment.
Color box size with black borders and text color. Standard size. or ORANGE {{Color box striped}} Striped color box. Standard size. {} Borderless color box with text color and wikilinks. ORANGE {} Colored bullet with wikilinks. {{Legend inline}} Color box size with black borders. Standard size. {{Color sample}}
The rainbow connection number of a graph is the minimum number of colors needed to rainbow-connect , and is denoted by (). Similarly, the strong rainbow connection number of a graph G {\displaystyle G} is the minimum number of colors needed to strongly rainbow-connect G {\displaystyle G} , and is denoted by src ( G ) {\displaystyle {\text{src ...
Finding ψ(G) is an optimization problem.The decision problem for complete coloring can be phrased as: . INSTANCE: a graph G = (V, E) and positive integer k QUESTION: does there exist a partition of V into k or more disjoint sets V 1, V 2, …, V k such that each V i is an independent set for G and such that for each pair of distinct sets V i, V j, V i ∪ V j is not an independent set.