22.2-5 example is incorrect

[faucct]

Your E_π adjacency lists:

1: 2, 4 2: 5 4: 3

It will be produced by running BFS on G with this adjacency lists:

1: 2, 4 2: 5, 3 4: 3, 5

Here is a correct example of E_π impossible to produce by running BFS no matter how the vertices are ordered in each adjacency list of G:

E_π adjacency lists:

1: 2, 3 2: 4, 5 3: 6 6: 7

G adjacency lists:

1: 2, 3 2: 4, 5 3: 5, 6 5: 7 6: 7