1) If it‘s a tree, it ain‘t got no loops 2) The stack isn‘t to deal with loops, the „visited“ flag at each edge is there for that. The stack (for DFS, BFS would be a queue) is there to keep track of which nodes have been visited such that you can construct a path from the starting node to the one you‘re looking for.

Obviously there are variants to this, depending on what you‘re actually trying to achieve with it. My point is that a stack would be a very inefficient way to deal with loops.