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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
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