In this section, we formulate the channel allocation problem using graph theory. We assume that the interference map among APs is known a priori. The interference relation among APs is assumed to be derived from the aggregated AP information reported back from APs/user devices. Each AP with its own bandwidth generates a neighbor AP list by overhearing, and reports the information to the APC. Then the APC can generate an invading map among the APs with the neighboring AP lists and bandwidth information. For example, if APa with 80 MHz senses the existence of APb with 20 MHz but not vice versa, then the APC can infer that they may suffer partial invading. Note again that we only consider the downlink scenario in this paper