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This paper considers the interaction between channel assignment and distributed scheduling in multi-channel multiradio Wireless Mesh Networks (WMNs). Recently, a number of distributed scheduling algorithms for wireless networks have emerged. Due to their distributed operation, these algorithms can achieve only a fraction of the maximum possible throughput. As an alternative to increasing the throughput fraction by designing new algorithms, in this paper we present a novel approach that takes advantage of the inherent multi-radio capability of WMNs. We show that this capability can enable partitioning of the network into subnetworks in which simple distributed scheduling algorithms can achieve 100% throughput. The partitioning is based on the recently introduced notion of Local Pooling. Using this notion, we characterize topologies in which 100% throughput can be achieved distributedly. These topologies are used in order to develop a number of channel assignment algorithms that are based on a matroid intersection algorithm. These algorithms partition a network in a manner that not only expands the capacity regions of the subnetworks but also allows distributed algorithms to achieve these capacity regions. Finally, we evaluate the performance of the algorithms via simulation and show that they significantly increase the distributedly achievable capacity region.