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Cognitive radio (CR) capitalizes advances in signal processing and radio technology and is capable of reconfiguring RF and switching to desired frequency bands. It is a frequency-agile data communication device that is vastly more powerful than recently proposed multi-channel multi-radio (MC-MR) technology. In this paper, we investigate the important problem of multi-hop networking with CR nodes. For such a network, each node has a pool of frequency bands (typically of unequal size) that can be used for communication. The potential difference in the bandwidth among the available frequency bands prompts the need to further divide these bands into sub-bands for optimal spectrum sharing. We characterize the behavior and constraints for such a multi-hop CR network from multiple layers, including modeling of spectrum sharing and sub-band division, scheduling and interference constraints, and flow routing. We develop a mathematical formulation with the objective of minimizing the required network-wide radio spectrum resource for a set of user sessions. Since the formulated model is a mixed-integer non-linear program (MINLP), which is NP-hard in general, we develop a lower bound for the objective by relaxing the integer variables and using a linearization technique. Subsequently, we design a near-optimal algorithm to solve this MINLP problem. This algorithm is based on a novel sequential fixing procedure, where the integer variables are determined iteratively via a sequence of linear programs. Simulation results show that solutions obtained by this algorithm are very close to the lower bounds obtained via the proposed relaxation, thus suggesting that the solution produced by the algorithm is near-optimal.