Questions tagged [vertex-cover]

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Compute the expected size of an approximation of vertex cover

Consider the following randomized approximation algorithm of vertex cover: Input: A graph G = (V, E). Output: A set $C_G \subseteq V$ a vertex cover of $G$. The algorithm: Set $C_G := \emptyset$. ...
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Dominating Set Gap Problem Reduction

In the reduction from Vertex Cover problem to Dominating Set a new vertex is added for each edge in the original graph. Specifically, Given graph $G=(V,E)$ where $|V|=n$ with $VC$ with size $k$ we ...
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Show that for each even n, there exists a graph with n vertices, such that the 2-approx VC alg returns a VC which is exactly twice the Minimum-VC

Question: Show that for each even n, there exists a graph with n vertices, such that the ALG(algorithm) returns a vertex cover which is exactly twice the size of minimum vertex cover. Define ALG: ...
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set cover to edge cover

I want to find set cover of this problem. I have sets, each of cardinality 3. I want to find set cover. This is what I am doing. Treat each set as an edge, which is incident on each of its element. I ...