How to find if a graph is bipartite?

Question

I have been trying to understand the bipartite graph. To my understanding it is a graph G which can be divided into two subgraphs U and V.So that intersection of U and V is

Answer 1

From Carnegie Mellon University:

"Recall that a graph G = (V, E) is said to be bipartite if its vertex set V can be partitioned into two disjoint sets V1, V2 such that all edges in E. have one endpoint in V1 and one endpoint in V2.

(source: http://www.cs.cmu.edu/~15251/homework/hw5.pdf)

Are you sure that you need to use BFS? Determining if a graph if bipartite requires detecting cycle lengths, and DFS is probably better for cycle detection than BFS.

Anyway, a graph if bipartite if and only if it has no cycles of odd length. If you're allowed to use DFS, you can DFS on the graph and check for back-edges to detect the presence of cycles and use DFS timestamps to compute the size of each cycle.