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Problem: Is Graph Bipartite?

Explore how to determine whether an undirected graph is bipartite by using breadth-first search to assign two colors without conflict. Understand the problem constraints, BFS-based approach, and how to detect odd cycles for disconnected graphs. This lesson helps you implement and analyze the bipartite graph problem efficiently.

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Statement

You are given an undirected graph with n nodes, numbered from 00 to n−1n - 1. The graph is represented as a 22D array graph, where graph[u] contains all nodes adjacent to node u. That is, for every v in graph[u], there exists an undirected edge between node u and node v.

The graph satisfies the following properties:

  • No self-loops exist (graph[u] does not contain u).

  • No parallel edges exist (all values in graph[u] are unique).

  • The graph is undirected: if v appears in graph[u], then u appears in graph[v].

  • The graph is not necessarily connected.

A graph is bipartite if its nodes can be partitioned into two independent sets A and B such that every edge in the graph connects a node in set A to a node in set B.

Return true if and only if the given graph is bipartite.

Constraints:

  • graph.length ==n== n ...