AbstractThe currently in use spectrum management policies are responsible for the poor utilization of the electromagnetic radio spectrum. By performing dynamic spectrum management (DSM), cognitive radio (CR) has the potential to increase the radio spectrum efficiency significantly and has gained a lot of attention recently. In this paper, we present an overview of the DSM problem in CR. After describing the CR briefly, the DSM is explained. In order to increase the spectrum utilization efficiency, CR tries to share the spectrum with primary users. We discuss two methods for spectrum‐sharing, namely price‐based spectrum‐sharing and opportunistic spectrum‐sharing. After introducing necessary mathematical definitions, the formulation of the DSM problem is presented. We show that the DSM problem is equivalent to a well‐known graph‐coloring problem (GCP) called list‐coloring. Finding the exact solution for this problem is computationally intensive and various approximate algorithms have been proposed to obtain suboptimum solutions. Finally, we discuss two approaches for solving the DSM problem: centralized approach and decentralized approach. Decentralized approach, although has complicated design and may not achieve the global optimum solution, is more suitable for CR due to scalability and lower complexity. Copyright © 2009 John Wiley & Sons, Ltd.