A graph is said to be bipartite if all its vertices can be partitioned into two
ID: 3847312 • Letter: A
Question
A graph is said to be bipartite if all its vertices can be partitioned into two disjoint subsets X and Y so that every edge connects a vertex in X with a vertex in Y. (One can also say that a graph is bipartite if its vertices can be colored in two colors so that every edge has its vertices colored in different colors;such graphs are also called 2-colorable.) For example, graph (i) is bipartite while graph (ii) is not. Design a DFS-based algorithm for checking whether a graph is bipartite. Design a BFS-based algorithm for checking whether a graph is bipartite.Explanation / Answer
import java.io.*;
import java.util.*;
// This class represents a directed graph using adjacency list
// representation
class Graph
{
private int V; // No. of vertices
private LinkedList<Integer> adj[]; //Adjacency Lists
// Constructor
Graph(int v)
{
V = v;
adj = new LinkedList[v];
for (int i=0; i<v; ++i)
adj[i] = new LinkedList();
}
// Function to add an edge into the graph
void addEdge(int v,int w)
{
adj[v].add(w);
}
// prints BFS traversal from a given source s
void BFS(int s)
{
// Mark all the vertices as not visited(By default
// set as false)
boolean visited[] = new boolean[V];
// Create a queue for BFS
LinkedList<Integer> queue = new LinkedList<Integer>();
// Mark the current node as visited and enqueue it
visited[s]=true;
queue.add(s);
while (queue.size() != 0)
{
// Dequeue a vertex from queue and print it
s = queue.poll();
System.out.print(s+" ");
// Get all adjacent vertices of the dequeued vertex s
// If a adjacent has not been visited, then mark it
// visited and enqueue it
Iterator<Integer> i = adj[s].listIterator();
while (i.hasNext())
{
int n = i.next();
if (!visited[n])
{
visited[n] = true;
queue.add(n);
}
}
}
}
// Driver method to
public static void main(String args[])
{
Graph g = new Graph(4);
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(1, 2);
g.addEdge(2, 0);
g.addEdge(2, 3);
g.addEdge(3, 3);
System.out.println("Following is Breadth First Traversal "+
"(starting from vertex 2)");
g.BFS(2);
}
}