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In this paper, the problems of relay selection and channel allocation in a cognitive two-way relay network are modelled as a classical weighted bipartite graph matching problem and are solved by the Hungarian algorithm. In the proposed radio resource management algorithm, firstly, some of cognitive radio (CR) nodes are selected to establish the primary user connection as a two-way relay scheme. Then, a power updating algorithm is used to give the maximum signal-to-interference-plus-noise ratio (SINR) in the CR nodes, while keeping the minimum SINR level at the primary transceivers and the best channel assignment is done for CR nodes in order to maximize the SINR value of them. Simulation results show that the proposed algorithm improves the performance of the whole network in comparison with conventional power allocation and relay selection algorithms.