Question: 1. What is the minimum number of nodes and arcs that need to be deleted to reduce a full binary tree of height ≥ 2 to a forest of 4 binary trees?
2. Let G be a simple graph. Prove that G is a nonrooted tree if and only if G is connected and if the removal of any single arc from G makes G unconnected
3. Let G be a simple graph. Prove that G is a nonrooted tree if and only if G is connected and the addition of one arc to G results in a graph with exactly one cycle?