Before revision:  Finally\texttt{  , we derive a tight universal regret lower bound for the\textsf{Bipartite Caching problem, which critically makes use of results from graph coloring theory and certifies the announced approximation ratio .
After revision:  Finally\texttt{ , we derive a tight universal regret lower bound for the\textsf{Bipartite Caching using results from graph coloring theory and certifies the announced approximation ratio .