C++ Program to Perform Graph Coloring on Bipartite Graphs

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. In this program we take a bipartite graph as input and outputs colors of each vertex after coloring the vertices.

Algorithm

Begin
   BFS algorithm is used to traverse all the vertices.
   Take a vertex and colour it yellow.
   Colour all its neighbour vertices as blue.
   Colour the next level vertices as yellow and so, until all vertices are coloured.
End.

Example Code

#include<bits/stdc++.h>
using namespace std;
int n, e, i, j;
vector<vector<int> > g;
vector<int> color;
bool v[11101];
void c(int node,int n) {
   queue<int> q;
   if(v[node])
      return;
   color[node]=n;
   v[node]=1;
   for(i=0;i<n;i++) {
      if(!v[g[node][i]]) {
         q.push(g[node][i]);
      }
   }
   while(!q.empty()) {
      c(q.front(),(n+1)%2);
      q.pop();
   }
   return;
}
int main() {
   int a,b;
   cout<<"Enter number of vertices and edges respectively:";
   cin>>n>>e;
   cout<<"'Y' is for Yellow Colour and 'B' is for Blue Colour.";
   cout<<"\n";
   g.resize(n);
   color.resize(n);
   memset(v,0,sizeof(v));
   for(i=0;i<e;i++) {
      cout<<"\nEnter edge vertices of edge "<<i+1<<" :";
      cin>>a>>b;
      a--; b--;
      g[a].push_back(b);
      g[b].push_back(a);
   }
   c(0,1);
   for(i=0;i<n;i++) {
      if(color[i])
         cout<<i+1<<" "<<'Y'<<"\n";
      else
         cout<<i+1<<" "<<'B'<<"\n";
   }
}

Output

Enter number of vertices and edges respectively:4 3
'Y' is for Yellow Colour and 'B' is for Blue Colour.

Enter edge vertices of edge 1 :1 2
Enter edge vertices of edge 2 :3 2
Enter edge vertices of edge 3 :4 2
1 Y
2 B
3 B
4 B