Quiz: Tree Centers

In the Minimum Height Trees problem, you repeatedly remove leaf nodes (degree $1$) until $1$ or $2$ nodes remain. Why does this give the center of the tree?

1. A.Leaves are always far from the center, so removing them has no effect
2. B.Removing leaves from all sides simultaneously peels the tree inward, converging on the midpoint of the longest path
3. C.The last leaf removed is always the node with the most children
4. D.This is a greedy heuristic that works most of the time but not always