CareerCup

We can do this by marking each node with 0 or 1.The first one we mark with 1, then a node in his list of neighbours with 0, then a neighbour of the neighbour with 1 and so until we mark all the nodes(and return true) or we arrive in a node that is 0 and we want to mark it with 1 or viceversa (and we return false).

public Boolean bipartite() {
Boolean flag = true;
for (Node u : graph.getNodes)
if(u.state == 0)
BDFS(u,1);// first vertex node
return flag;
}
public void Boolean BDFS(Node u,int c) {
u.state = c;
for (Node v: graph.getadjacent())
if (v.state == 0)
BDFS(v,-c);
else if(v.state == c) return false;

}

2 coloring..which is essentially the same solution mentioned by bog dan.cebere

geeksforgeeks.org/bipartite-graph/

This can be done using DFS. I'm not sure though if its the most efficient way.

// source: google
   for all v in V do visited(v) = 0
   for all v in V do if (visited(v)==0) DFS(v,0)

   DFS(v,p) {
      visited(v) = 1
      part(v) = p
      for all w in adj(v) do {
          if (visited(w)==0) {
              DFS(w,1-p)
          } else {
              if (part(v) == part(w)) print "graph not bipartite"
          }
      }
   }