# Check if Graph is Bipartite – Adjacency List using Breadth-First Search(BFS)

**Objective: **Given a graph represented by the adjacency List, write a Breadth-First Search(BFS) algorithm to check whether the graph is bipartite or not.

Earlier we have solved the same problem using Depth-First Search (DFS). In this article, we will solve it using Breadth-First Search(BFS). Before we proceed, if you are new to Bipartite graphs, lets brief about it first

**Bipartite Graphs** OR **Bigraphs** is a graph whose vertices can be divided into two independent groups or sets so that for every edge in the graph, each end of the edge belongs to a separate group. There should not be any edge where both ends belong to the same set. Please read “Introduction to **Bipartite Graphs** OR **Bigraphs“.**

**Example:**

Please read the following recommended articles before continue

**Approach:** Coloring of vertices – Check if Graph Two-Colorable using BFS

Choose three colors- ** RED**,

**,**

*GREEN***. As you know in Bipartite graph, both ends of each edge belong to separate group, Let’s say here two groups are**

*WHITE***and**

*RED***and for a graph to be bipartite, for each edge- one end has to be**

*GREEN***and another end has to be**

*RED***.**

*GREEN*- Initially color all the vertices in
and as algorithm advances, these vertices will be colored as*WHITE*or*RED*.*GREEN* - Initialize queue.
- Pick a vertex with color
, now color it with*WHITE*. Add it to the queue.*RED* - While the queue is not empty
- take out a vertex from the queue. let’s say its vertex
.*v* - Now check all the neighbors of vertex
.*v*- If these neighbors are in
color, color them with the alternate color of vertex*WHITE*means if*v*is RED, color the neighbors in*v*and if*GREEN*is*v*, color the neighbors in*GREEN*. and add these neighbors in the queue.*RED* - If any of these neighbors are not in
color, which means it was already colored earlier, check its color and if it has the same color as vertex v that means vertices connecting v and this neighbor cannot be in two colors means the graph is not bipartite. return false.*WHITE*

- If these neighbors are in

- take out a vertex from the queue. let’s say its vertex
- Do steps 3 and 4 until all the vertices are in either
or*RED*color if that happens means graph is bipartite.*GREEN*

**Time Complexity**– O(V+E)

**Code:**

**Output:**

Graph is Bipartite: false -------------------------- Graph is Bipartite: true