Bipartite Graph Check in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a bipartite graph?

A bipartite graph is a graph whose nodes can be divided into two groups such that no two nodes within the same group are connected by an edge.

beginner

Which method is commonly used to check if a graph is bipartite?

We use graph coloring with two colors or BFS/DFS to check if the graph can be colored without conflicts, meaning no two adjacent nodes share the same color.

beginner

In bipartite graph check, what does it mean if a conflict in coloring is found?

It means the graph is not bipartite because two connected nodes have the same color, breaking the rule of bipartite division.

beginner

Why do we use two colors in bipartite graph checking?

Two colors represent the two groups of nodes. Assigning colors helps verify if nodes can be separated without edges inside the same group.

intermediate

What is the time complexity of checking if a graph is bipartite using BFS or DFS?

The time complexity is O(V + E), where V is the number of vertices and E is the number of edges, because each node and edge is visited once.

What does it mean if a graph is bipartite?

A Its nodes can be split into two groups with no edges inside the same group

B It has an equal number of nodes and edges

C It contains a cycle of odd length

D All nodes are connected to each other

A bipartite graph can be divided into two groups with edges only between groups, not inside.

Which algorithm is commonly used to check bipartite property?

A Dijkstra's algorithm

B Prim's algorithm

C BFS or DFS with two-coloring

D Topological sort

BFS or DFS with two-coloring helps detect if adjacent nodes can be colored differently.

If two adjacent nodes have the same color during bipartite check, what does it indicate?

A Graph is bipartite

B Graph is not bipartite

C Graph is complete

D Graph is disconnected

Same color on adjacent nodes breaks bipartite rules, so graph is not bipartite.

What is the minimum number of colors needed to check if a graph is bipartite?

A 4

B 1

C 3

D 2

Two colors represent the two groups in a bipartite graph.

What is the time complexity of bipartite graph check using BFS or DFS?

A O(V + E)

B O(E^2)

C O(V^2)

D O(log V)

Each vertex and edge is visited once, so complexity is O(V + E).

Explain how BFS or DFS can be used to check if a graph is bipartite.

Think about coloring nodes while traversing the graph.

Describe what a bipartite graph is and why two colors are used in its check.

Imagine separating people into two teams with no friends inside the same team.