The tremendous increasing demand to support various data applications requires a wireless network to be more agile and spectral-efficient. Cognitive Radio technology allows secondary users to access the underutilized licensed bands and is a promising solution. However, the coexistence of secondary users with the authorized primary users requires careful and dynamic resource management to deal with interference, which is a very challenging issue. The major objective of this project is to deal with the issue by utilizing graph theory/algorithms to develop efficient resource management schemes for general coexistence scenarios.