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Graph coloring

 

Graph Coloring


A graph G(V, E) is given and some colors are given


We have to color the vertices such that no two neighbours/adjacent vertices have the same color. This can be solved using Backtracking.


There are two types of problem


1.  m-colorability decision problem


If a graph G(V, E) is given and some colors are also given and just we want to know whether a graph can coloured using those colors or not. This is known as the m-coloring decision problem.


2.  m-colorability optimization problem


If a graph G(V, E) is given and we want to know minimum how many colors required for coloring the graph. This problem is called the m-coloring optimization problem.


Chromatic Number: The smallest number of colors needed to color a graph G is called its chromatic number.

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