Bipartite Graph Check in DSA Typescript - 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 so that no edge connects nodes within the same group.

beginner

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

We use graph coloring with two colors or Breadth-First Search (BFS) or Depth-First Search (DFS) to assign colors and check for conflicts.

beginner

In bipartite graph check, what does it mean if a node's neighbor has the same color?

It means the graph is not bipartite because two connected nodes share the same group, which is not allowed.

beginner

What data structure is useful to keep track of node colors during bipartite check?

An array or map to store colors for each node, typically using two values like 0 and 1 or -1 for uncolored.

intermediate

Why do we need to check all nodes in the graph when checking bipartiteness?

Because the graph might be disconnected, so we must check each connected component separately.

What is the main property of a bipartite graph?

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

B Every node connects to every other node

C Graph has no edges

D Graph contains cycles only

A bipartite graph's nodes can be divided into two groups with edges only between groups.

Which algorithm is commonly used to color nodes for bipartite check?

A Floyd-Warshall algorithm

B Dijkstra's algorithm

C Prim's algorithm

D Breadth-First Search (BFS)

BFS helps assign colors level by level to check bipartiteness.

If a neighbor node has the same color during bipartite check, what does it mean?

A Graph is bipartite

B Graph is not bipartite

C Graph is disconnected

D Graph is complete

Same color neighbors mean the graph is not bipartite.

What color value is usually used to mark uncolored nodes?

A -1

B 1

C 0

D 2

Uncolored nodes are often marked with -1 to distinguish from colored nodes.

Why must we check all nodes in the graph for bipartite property?

A Because nodes have weights

B Because all nodes have edges

C Because graph might be disconnected

D Because graph is always connected

Disconnected graphs have multiple components that must be checked separately.

Explain how to check if a graph is bipartite using BFS.

Think about coloring nodes level by level and checking conflicts.

Describe why a graph with an odd-length cycle cannot be bipartite.

Consider coloring nodes around a cycle and what happens at the end.