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problemset9 solutions

# Assume for the sake of contradiction if is that the

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Unformatted text preview: have that � � � � for a binary tree and any with � � . Thus, �  � tree is strongly ���� �-separable, meaning that it can be cut exactly in half by cutting � � � � �� �� � ����� � � � � ������ � . So the binary tree can be cut in Now, we consider the constants. We have that �  � � half by cutting at most ������ � � �� edges. We can compute the appropriate constants by changing the base of the ���. � nodes, �� � Lemma 6Given a binary tree with � nodes and an input � , with � � � � �, there is a cut of a single edge that cuts off between � �� and � nodes. For a binary tree, there is also a simple more direct 4 approach. Basically, i claim that for any binary tree with and a given number , with � , I can cut off a subtree with between � and nodes with a single cut. � �� Proof. Consider the depth (distance from root) of every node in the tree. Iterate through all the nodes i...
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