Modify BFS to only use a single bit to represent a vertexs label (right now the labels have three possibilities, which requires two bits). Argue that the modified algorithm still works correctly.

BFS (G, s) 1 for each vertex u e G.V -{s) 2 ucolor WHITE 4 5 s.color= GRAY 9 ENQUEUE Q,s 10 while ? u = DEQUEUE(Q) 12 for each v E G.Adj[u] 13 if v. color == WHITE V,color = GRAY 15 16 17 18 ENQUEUE(Q, v) . Color BLACK