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One of the challenges in Multi-Radio Multi-Channel Wireless Mesh Networks is the assignment of channels to links such that connectivity is ensured and interference is minimized. Two links that are within interference range of each other could be assigned the same channel, which causes co-channel interference and decreases network throughput. In this paper, we identify the above problem in the Topology-controlled Interference-aware Channel-assignment Algorithm (TICA)  and propose an enhanced version called e-TICA. The new algorithm solves the un-foreseen interference problem through two-way interference-range edge coloring. We show through simulations that e-TICA outperforms TICA in terms of fairness among flows without sacrificing the average network throughput.