Matching 2f upper bound for vertex faults

Prove or disprove that every n-node weighted graph admits an f-vertex fault-tolerant k-spanner with vertex-competitive lightness using competition parameter $2f$ and bound $O(\operatorname{poly}(f)\cdot\lambda(n,k+1))$.

Background

The authors identify 2f as the necessary lower bound on the vertex competition parameter, but their connected-dominating-set approach yields only a competition parameter of order f log n and faces additional connectivity obstacles. They therefore leave unresolved whether the lower bound 2f can be achieved by an upper-bound construction.