problemset9 solutions

# Thus tree is strongly separable meaning that it can be

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Unformatted text preview: � ��. Applying Lemma 2, we get ���� � ������� � ��� � �. Note that the above proof does not depend on the ordering of leaves in the VLSI layout. That is to say, the leaves of the two �-leaf subtrees of an -leaf VLSI layout can be interleaved and reordered arbitrarily without affecting correctness of the proof. �� � Problem 9-3. Show that any binary tree with an even number of nodes can be cut exactly in half by cutting edges. What is the constant? Solution: That a binary tree with an even number of nodes can be cut exactly in half by cutting follows directly from lecture on April 21. We have the following two lemmas from class: ����� �� ����� �� edges Lemma 4Binary trees are �-separable. Lemma 5If a graph � is � -separable, then � is strongly �  -separable. In class, we deﬁned � ������ � � � � � � �� ��� � �� � � � � � � �� � �� � ����� ��, and a binary ����� �� edges. By Lemma 4, we...
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