I have an algorithm that solves the Vertex Cover problem. The algorithm is
Repeat while there is an edge:
Arbitrarily pick an uncovered edge $e = uv$ and add $u$ and $v$ to the solution. Delete $u$ and $v$ from the graph.
I know this strategy is a 2-approximation to Vertex Cover and that its worst example is the complete bipartite graph $K_{n,n}$. In this graph, the algorithm will return a vertex cover of size $2n$ whereas the optimal solution is of size $n$.
Question: Does there exist a graph with Minimum Vertex Cover of size 10 where this strategy finds a minimum vertex cover?