Consider the following decision problems:
– Minimum-Spanning-Tree: Given a weighted graph G = (V;E) and aninteger d, does there exist a
spanning tree of G with weight at most d?
– Minimum-Spanning-2-Forest: Given a weighted graph G = (V;E) andan integer d, does there exist
a pair of subtrees T1 = (V1;E1)and T2 = (V2;E2) of G, such thatV2 = V V1 (i.e. each vertex of
G is in either T1 or T2), and the weight ofthe two trees sum to at most d?
(i) Prove that Minimum-Spanning-2-Forest 
p Minimum-Spanning-Tree (you may assume that the
weights are positive and that the graph has at
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