We study the problem of achieving maximum network throughput with fairness among the flows at the nodes in a wireless mesh network, given their location and the number of their half-duplex radio interfaces. Our goal is to find the minimum number of non-overlapping frequency channels required to achieve interference-free communication. We use our existing Select x for less than x topology control algorithm (TCA) to build the connectivity graph (CG), which enhances spatial channel reuse to help minimize the number of channels required. We show that the TCA-based CG approach requires fewer channels than the classical approach of building the CG based on the maximum power. We use multi-path routing to achieve the maximum network throughput and show that it provides better network throughput than the classical minimum power-based shortest path routing. We also develop an effective heuristic method to determine the minimum number of channels required for interference-free channel assignment.