# Variant of greedy algorithm for vertex cover

Does the following approximation algorithm for vertex cover also have an approximation ratio of 2? Why? Why not?

Input: $$G = (V,E)$$

1. Set $$C \gets \emptyset$$ and $$E’ \gets E$$.
2. while $$E’ \neq \emptyset$$ do:
• Pick any edge $$(u,v) \in E’$$.
• $$C \gets C \cup \{u\}$$.
• Remove from $$E’$$ all edges incident to $$u$$.
3. return $$C$$.