Graph Coloring Minimum Number Of Colors

Graph Coloring Minimum Number Of Colors. Star coloring definitely satisfies the conditions but it needs more colors. In a graph, no two adjacent vertices, adjacent edges, or adjacent regions are colored with minimum number of colors.

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If a graph is properly colored, the vertices that are assigned a particular color form an independent set. Our color is to find a coloring of a given graph that uses the minimum number of colors. Chromatic Number is the minimum number of colors required to properly color any graph.

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.

A color assignment with this property is called a valid coloring of the graph—a "coloring," for short.

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It presents a number of instances with best known lower bounds and upper bounds. The usual goal, and the one considered here, is to color every vertex of a graph such that adjacent vertices get dierent colors. Star coloring definitely satisfies the conditions but it needs more colors.