This paper investigates the user grouping problem of downlink wireless local area networks (WLANs) with multi-user MIMO (MU-MIMO). Particularly, we focus on the problem of whether single user transmit beamforming (SU-TxBF) or MU-MIMO should be utilized, and how many users and which users should be in a multi-user (MU) group. We formulate the problem for maximizing the system throughput subject to the multi-user air time fairness (MU-ATF) criterion. We show that hypergraphs provide a suitable mathematical model and effective tool for finding the optimal or close to optimal solution. We show that the optimal grouping problem can be solved efficiently for the case where only SU-TxBF and 2-user MU groups are allowed in the system. For the general case, where any number of users can be assigned to groups of different sizes, we develop an efficient graph matching algorithm (GMA) based on graph theory principles. We evaluate the proposed algorithm in terms of system throughput using an 802.11ac emulator, which is created using collected channel measurements from an indoor environment and simulated channel samples for outdoor scenarios. We show that our GMA achieves at least 93% of the optimal system throughput in all considered test cases.