Online social networks have become an effective and important social platform for communication, opinions exchange, and information sharing. However, they also make it possible for rapid and wide misinformation diffusion, which may lead to pernicious influences on individuals or society. Hence, it is extremely important and necessary to detect the misinformation propagation by placing monitors. In this article, we first define a general misinformation-detection problem for the case where the knowledge about misinformation sources is lacking, and show its equivalence to the influence-maximization problem in the reverse graph. Furthermore, considering node vulnerability, we aim to detect the misinformation reaching to a specific user. Therefore, we study a τ-Monitor Placement problem for cases where partial knowledge of misinformation sources is available and prove its #P complexity. We formulate a corresponding integer program, tackle exponential constraints, and propose a Minimum Monitor Set Construction (MMSC) algorithm, in which the cut-set2 has been exploited in the estimation of reachability of node pairs. Moreover, we generalize the problem from a single target to multiple central nodes and propose another algorithm based on a Monte Carlo sampling technique. Extensive experiments on real-world networks show the effectiveness of proposed algorithms with respect to minimizing the number of monitors.