We introduced graph coloring and applications in previous post. As discussed in the previous post, graph coloring is widely used. Unfortunately, there is no efficient algorithm available for coloring a graph with minimum number of colors as the problem is a known NP Complete problem. 

There are approximate algorithms to solve the problem though. Following is the basic Greedy Algorithm to assign colors. It doesn’t guarantee to use minimum colors, but it guarantees an upper bound on the number of colors. 

The basic algorithm never uses more than d+1 colors where d is the maximum degree of a vertex in the given graph.

Graph Coloring : https://www.geeksforgeeks.org/graph-coloring-set-2-greedy-algorithm/