— IEEE 802.11 Wi-Fi equipment based wireless mesh networks have recently been proposed as an inexpensive approach to connect far-flung rural areas. Such networks are built using high-gain directional antenna that can establish long-distance point-point links. In recent work [16], a new MAC protocol named 2P has been proposed that is suited for the interference pattern within such a network. However, the 2P protocol requires the underlying graph (for each 802.11 channel) to be bi-partite. Under the assumption that 2P is the MAC protocol used in the mesh network, we make the following contributions in this paper. Given K non-interfering 802.11 channels, we propose a simple cut-based algorithm to compute K bi-partite sub-graphs (on each of which the 2P protocol can be run separately). We establish the class of graphs that can thus be completely covered by K bipartite subgraphs. For the remaining set of graphs, we look into the “price” of routing all end-to-end demands over only the...