Abstract: Active-passive hybrid radar systems make full use of passive signals in the environment and integrate the advantages of active radar and passive radar, enabling efficient radar detection in the increasingly complex electromagnetic environment. Focusing on the target detection problem of active-passive hybrid radar systems, this paper investigates the antenna selection and discrete power allocation for active radar as well as the antenna selection for passive radar. To maximize the target detection performance subject to the constraints on the total transmit power of the active radar, the number of active antennas and passive antennas to be processed. a joint optimization problem with the detector output signal-to-noise ratio (SNR) as the performance metric is formulated based on graph theory. The original problem is a nonlinear integer programming problem, whose computational complexity increases drastically with the growth of the number of active and passive transmit antennas. In this paper, the selection of passive antennas is regarded as a vertex set in a bipartite graph, and the joint optimization of antenna selection and transmit power allocation for active radar is transformed into a matching problem between two vertex sets, converting the joint discrete optimization problem into a stable matching problem. Accordingly, a joint optimization algorithm based on the Gale-Shapley (GS) algorithm is proposed. Simulation results demonstrate that the proposed algorithm significantly reduces the computational complexity while achieving near-optimal target detection performance.