Bipartite Graph — Color It, Don’t Fight It

Shreyas Naphad
Jul 12
1 min read

Let’s say you’re forming two teams from a group of people, where some people just can’t work together. Your job is to split them into two groups so that no enemies end up on the same team.

This is what a bipartite graph is about.

🧠 Definition

A graph is bipartite if its nodes can be split into two sets such that no two nodes in the same set are connected.

Equivalently: it can be 2-colored without adjacent nodes having the same color.

🛠️ How to Check for Bipartiteness?

Use BFS or DFS and try to color the graph using 2 colors.

If you ever find two adjacent nodes with the same color — ❌ not bipartite.

🚦 BFS-Based Algorithm

🎯 Common Use Cases

Team or group partitioning
Matching problems (job-person match, stable marriage)
Checking if a graph can be divided cleanly

💥 Classic Interview Problems

“Is the graph bipartite?”
“Split nodes into two groups without conflicts.”
“Can we schedule tasks with dependency restrictions?”

📚 Pro Tips

Works on both connected and disconnected graphs — just check each component.
Use DFS if you want recursion-based flavor.

✅ Final Thought

Bipartite graphs are about balance — no drama, just clear divisions.

If your graph can be painted in two colors without overlap — congratulations, you just mastered bipartiteness