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My question today is about the approximation algorithms. Well, for Approx-Vertex-Cover problems , we know we can get ratio of 2 just by picking an edge and taking 2 endpoints of the same and continuing this process.

A new way to do the same is, to create a DFS first and then take non-leaf nodes which will be a vertex cover.

I wanted to ask is there any family of graphs for which I can get a ratio of 2 for approximation using DFS ?

Thanks, Snehal

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