Given a full binary tree of size $n$, I need to cut the tree into two by choosing an edge and removing it. I want the cutting to be as equal as possible (i.e. the two subtrees have as equal weight as possible).
Can I always cut the tree into two equal subtrees? If not, what is the lower bound for the cut (the smallest size of the smaller subtree)?
What is an algorithm I can use to find this cut?