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A novel, practical and low-complexity multi-cell OFDMA downlink channel assignment method using a graph- based approach is proposed in this work. The inter-cell interference (ICI) information is obtained through inference from the diversity set of mobile stations (MSs) and presented in the form of an interference graph. The proposed downlink channel assignment method consists of two phases. The task of ICI reduction is mapped to the MAX fe-CUT problem in graph theory and solved in the first phase. Then, channel assignment is conducted by taking into account instantaneous channel conditions in the second phase. State-of-the-art ICI management techniques such as ICI coordination (ICIC) and base station cooperation (BSC) are incorporated in our framework. Heuristic algorithms are proposed to solve both phases of the problem efficiently. Simulation is conducted to demonstrate the effectiveness of the proposed solution, where the SINR improvement can be as high as 4.5 dB. The proposed solution can be used in next generation cellular systems such as 3 GPP long term evolution (LTE) and IEEE 802.16 m.