Check if a given graph is Bipartite using DFS

Given a connected graph, check if the graph is bipartite or not. A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color. Note that it is possible to color a cycle graph with even cycle using two colors. For example, see the following graph.

It is not possible to color a cycle graph with an odd cycle using two colors.

In the previous post, an approach using BFS has been discussed. In this post, an approach using DFS has been implemented. Given below is the algorithm to check for bipartiteness of a graph.

Use a color[] array which stores 0 or 1 for every node which denotes opposite colors.
Call the function DFS from any node.
If the node u has not been visited previously, then assign !color[v] to color[u] and call DFS again to visit nodes connected to u.
If at any point, color[u] is equal to !color[v], then the node is bipartite.
Modify the DFS function such that it returns a boolean value at the end.

Below is the implementation of the above approach:

// C++program to check if a connected 
// graph is bipartite or not suing DFS 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to store the connected nodes 
void addEdge(vector<int> adj[], int u, int v) 
{ 
    adj[u].push_back(v); 
    adj[v].push_back(u); 
} 
  
// function to check whether a graph is bipartite or not 
bool isBipartite(vector<int> adj[], int v, 
                 vector<bool>& visited, vector<int>& color) 
{ 
  
    for (int u : adj[v]) { 
  
        // if vertex u is not explored before 
        if (visited[u] == false) { 
  
            // mark present vertic as visited 
            visited[u] = true; 
  
            // mark its color opposite to its parent 
            color[u] = !color[v]; 
  
            // if the subtree rooted at vertex v is not bipartite 
            if (!isBipartite(adj, u, visited, color)) 
                return false; 
        } 
  
        // if two adjacent are colored with same color then 
        // the graph is not bipartite 
        else if (color[u] == color[v]) 
            return false; 
    } 
    return true; 
} 
  
// Driver Code 
int main() 
{ 
    // no of nodes 
    int N = 6; 
  
    // to maintain the adjacency list of graph 
    vector<int> adj[N + 1]; 
  
    // to keep a check on whether 
    // a node is discovered or not 
    vector<bool> visited(N + 1); 
  
    // to color the vertices 
    // of graph with 2 color 
    vector<int> color(N + 1); 
  
    // adding edges to the graph 
    addEdge(adj, 1, 2); 
    addEdge(adj, 2, 3); 
    addEdge(adj, 3, 4); 
    addEdge(adj, 4, 5); 
    addEdge(adj, 5, 6); 
    addEdge(adj, 6, 1); 
  
    // marking the source node as visited 
    visited[1] = true; 
  
    // marking the source node with a color 
    color[1] = 0; 
  
    // Function to check if the graph 
    // is Bipartite or not 
    if (isBipartite(adj, 1, visited, color)) { 
        cout << "Graph is Bipartite"; 
    } 
    else { 
        cout << "Graph is not Bipartite"; 
    } 
  
    return 0; 
} 

Output:

Graph is Bipartite

Time Complexity: O(N)
Auxiliary Space: O(N)

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