# Greedy algorithm for vertex cover

Given a graph $$G(V, E)$$, consider the following algorithm:

1. Let $$d$$ be the minimum vertex degree of the graph (ignore vertices with degree 0, so that $$d\geq 1$$)
2. Let $$v$$ be one of the vertices with degree equal to $$d$$
3. Remove all vertices adjacent to $$v$$ and add them to the proposed vertex cover
4. Repeat from step 1. until in $$G$$ there are only vertices with degree $$0$$ (no edges in the graph)

At the end the removed vertices are a vertex cover of the given $$G(V, E)$$, but is it a minimum vertex cover? Is there an example where the algorithm does not find a minimum vertex cover?