# C++ Program to Check whether Graph is a Bipartite using 2 Color Algorithm

A bipartite graph is a graph in which if the graph coloring is possible using two colors i.e.; vertices in a set are colored with the same color. This is a C++ program to Check whether a graph bipartite or not using 2 color algorithm.

## Functions and pseudocodes

Begin
1. Develop function isSafe() to check if the current color assignment
is safe for vertex v, i.e. checks whether the edge exists or not.
If it exists, then next check whether the color to be filled in
2. function graphColoringtil(bool g[V][V], int k, int col[], int v) :
g[V][V] = It is a 2D array where V is the number of vertices in graph
k = maximum number of colors that can be used.
col[] = an color array that should have numbers from 1 to m.
if v == V
return true
For c = 1 to k
if (isSafe(v, g, col, c))
col[v] = c
if (graphColoringtil (g, k, col, v+1) == true)
return true
col[v] = 0
return false
3.function graphColoring(bool g[V][V], int k):
for i = 0 to V-1
color[i] = 0
if (graphColoringtil(g, k, color, 0) == false)
return false
return true

## Example

#include <iostream>
#include <cstdio>
#define V 4
using namespace std;
bool isSafe (int v, bool g[V][V], int col[], int C) //to solve m coloring //problem
{
for (int i = 0; i < V; i++)
if (g[v][i] && C == col[i])
return false;
return true;
}
bool graphColoringtil(bool g[V][V], int k, int col[], int v)
{
if (v == V) //If all vertices are assigned a color then
return true;
for (int c = 1; c <= k; c++) //Consider this vertex v and try different colors
{
if (isSafe(v, g, col, c)) //Check if assignment of color c to v is fine
{
col[v] = c;
if (graphColoringtil (g, k, col, v+1) == true) //recur to assign colors to rest of the vertices
return true;
col[v] = 0; //If assigning color c doesn't lead to a solution then remove it
}
}
return false;
}

## Output

The graph is Bipartite