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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.
No matter which colors are chosen for the three central vertices, one of the outer 27 vertices will be uncolorable, showing that the list chromatic number of K 3,27 is at least four. More generally, let q be a positive integer, and let G be the complete bipartite graph K q,q q. Let the available colors be represented by the q 2 different two ...
Example of a four-colored map A four-colored map of the states of the United States (ignoring lakes and oceans). In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color.
This is an accepted version of this page This is the latest accepted revision, reviewed on 14 December 2024. For other color lists, see Lists of colors. This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "List of colors" alphabetical ...
The numbers of vertices in any two color classes differ by at most one. That is, the partition of vertices among the different colors is as uniform as possible. For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring.
This is an accepted version of this page This is the latest accepted revision, reviewed on 11 January 2025. Colors are an important part of visual arts, fashion, interior design, and many other fields and disciplines. The following is a list of colors. A number of the color swatches below are taken from domain-specific naming schemes such as X11 or HTML4. RGB values are given for each swatch ...
The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color.
The paths and even cycles of each subgraph may be colored with two colors per subgraph. After this step, each remaining odd cycle contains at least one edge that may be colored with one of the two colors belonging to the opposite subgraph. Removing this edge from the odd cycle leaves a path, which may be colored using the two colors for its ...