Graph Coloring is a special case of Graph Labelling, a fundamental problem in Graph Theory. It involves assigning colors to the vertices of a graph such that no two adjacent vertices share the same color. Here are some key aspects:
In Graph Coloring, each vertex in the graph is assigned a color from a finite set of colors. The goal is to use as few colors as possible while ensuring that adjacent vertices (those connected by an edge) do not share the same color. This concept is known as proper vertex coloring.
Graph coloring has numerous applications:
The Chromatic Number of a graph is the smallest number of colors needed to color the graph. Determining this number can be computationally complex, and for some graphs, it remains an open problem.
Graph coloring is an NP-Complete problem, meaning that for large graphs, finding the optimal coloring is computationally challenging. However, there are polynomial-time algorithms for specific classes of graphs or approximate solutions.
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