ps4 - (a) Show that minimum vertex cover is xed-parameter...

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6.889: Algorithms for Planar Graphs and Beyond October 5, 2011 Problem Set 4 This problem set is due Wednesday, October 12 at noon. 1. (a) Show that if C is the vertex set of a clique in a graph G , then the treewidth of G is at least | C | - 1. (b) Show that if the treewidth of a graph G is k , then G has a vertex of degree at most k . 2. In class we presented Baker’s technique using minimum vertex cover as an example. In this problem we fill in the missing details.
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Unformatted text preview: (a) Show that minimum vertex cover is xed-parameter tractable with respect to branch-width by describing a dynamic program (give pseudo-code). (b) Recall that G ij is the graph induced by vertices at breadth-rst-search levels jk + i through ( j + 1) k + i . Explain why a solution to the rst part can be used to nd a minimum vertex cover of G ij in 2 O ( k ) n time....
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