In relay-enabled cellular networks, the intertwined nature of network agents calls for complex schemes to allocate wireless resources. Resources need to be distributed among mobile users while considering how relay resources are allocated, and constrained by the traffic rate achievable by base stations and over backhaul links. In this letter, we derive an exact resource allocation scheme that achieves max-min fairness across mobile users, found with a linear complexity with respect to the number of mobile users and relays. The results reveal that the proposed scheme remarkably outperforms current solutions.