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Unformatted text preview: Instance: An undirected graph G = ( V,E ) and an integer 0 k | V | . Question: Is there a subset I V of vertices such that | I | k and no two vertices in I are adjacent ( independent set )? [Hint: If C is a vertex cover for G , what can you say about V-C ? If I is an independent set for G , what can you say about V-I ?] (not in text) Give a polynomial reduction from INDEPENDENT SET to CLIQUE. [Hint: The complement of an undirected graph G = ( V,E ) is the graph G = ( V,E ) where ( u,v ) E i ( u,v ) / E , for all distinct vertices u,v V .] (not in text) (more challenging) Give a polynomial reduction from (directed) HC to HAM-CYCLE (the undirected version of the Hamiltonian path problem (page 979)). [Hint: Given an instance G of HC, build a new graph G by replacing each vertex of G with a path of length 2. Connect endpoints of dierent paths together with edges in some way based on the edges of G .] 1...
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This note was uploaded on 12/13/2011 for the course CSCE 750 taught by Professor Fenner during the Fall '11 term at South Carolina.
- Fall '11