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

The following is a BFS approach to check whether the graph is bipartite.

• c = 0
• pick a node x and set x.class = c
• let ys be the nodes obtained by BFS
  • c = 1-c
  • for y in ys set y.class = c
  • if any y in ys has a neighbour z with z.class == c then the graph is not bipartite
  • repeat until no more nodes are found
• the graph is bipartite

This assumes that the graph is a single connected component -- if it is not, simply do this procedure for each component.