I came across this paragraph on wikipedia page:. Furthermore, there is a simple algorithm that maps a dominating set to a set cover of the same size and vice versa. Finding a dominating set of size k plays a central role in the theory of parameterized complexity. Sign up using Email and Password. Adding to this the set of smallest non-independent dominating set makes set of smallest dominating set.
On the other hand, if the input graph is planar, the problem remains NP-hard, but a fixed-parameter algorithm is known.
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In the first sentence "smallest" applies to the sets, which requires a unique minimal set as I've just re-iterated. I understand that minimal dominating sets can be either independent or not-independent. Similarly smallest dominating sets can be either independent or non-independent. In each example, each white vertex is adjacent to at least one red vertex, and it is said that the white vertex is dominated by the red vertex. This proved the dominating set problem to be NP-complete as well. I guess it should be "greater than or equal", right?