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Given an undirected graph $G$, where nodes represent towns and edges represent roads, and given a positive integer $k$, is there a way to build $k$ McDonald's at $k$ different towns so that every town either has its own McDonald's, or is connected by a (direct) road to a town that does have a McDonald's?

I believe that this problem is NP-complete. I am trying to find a well-known NP-complete problem, so I can use it to prove that this problem is NP-complete, too. Any suggestions?

Rodrigo de Azevedo
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This problem is called Dominating Set, and as pointed out by Raphael in the comments it's a special case of Set Cover (for each vertex, create a set for it and its neighbours). It's NP-hard.

j_random_hacker
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