How large does the stack S get?

Let a be the average size of an adjacency list Adj[u].

Let d be the current distance from the start vertex in the search.

When d is:		The size of S is:
0		1
1		a
2		O(a + a)

At each depth of the search, only the vertices u along the chosen path, and their undiscovered siblings on Adj[u], are stored.