Unformatted text preview: S | ) . 1. Show that the minimum connected dominating set problem admits a PTAS in apex-minor-free graphs. A dominating set in a graph G is a set D ⊆ V ( G ) such that D ∪ N ( D ) = V ( G ), where N ( D ) is the set of all vertices that are neighbors of some vertex of D . It is called a connected dominating set if G [ D ] is connected. 2. Show that the connected vertex cover problem admits a PTAS in H-minor-free graphs. Recall that a vertex cover in a graph is a set of vertices Z such that every edge of the graph has at least one endpoint in Z ; it is called a connected vertex cover if G [ Z ] is connected....
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This note was uploaded on 01/20/2012 for the course CS 6.889 taught by Professor Erikdemaine during the Fall '11 term at MIT.
- Fall '11