785 · Is Graph Bipartite?

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

2-Coloring Simulation

idle

INVARIANT 2-Coloring / Odd-Cycle Invariant: A graph is bipartite if and only if it contains 0 odd-length cycles. Traverse with BFS/DFS assigning alternating colors 0 (Blue) and 1 (Amber). If any neighboring node already shares the same color, an odd cycle is exposed → return false.

Current Node:-

Colors:[]

Conflict:None

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Java 21 Solution (BFS)

INTERVIEW SCRIPT

How to Explain Is Graph Bipartite to an Interviewer

1. The Odd Cycle Theorem

"A graph is bipartite if and only if it has no odd cycles. Bipartite checking is equivalent to 2-coloring: adjacent nodes must have different colors."

2. Multi-Component Handling

"The graph might be disconnected! We must iterate $i$ from 0 to $n-1$. If node $i$ is uncolored, start a new 2-coloring search assigning color[i] = 0."

3. Neighbor Color Checking

"For node $u$, iterate neighbors $v$: if $v$ is uncolored, assign color[v] = 1 - color[u] and enqueue. If $v$ is already colored and color[v] == color[u], return false immediately."

4. Complexity Mastery

"Every vertex and edge is visited at most once. Time complexity is $O(V + E)$ and space is $O(V)$ for the color array and BFS queue."