Visible light communication (VLC) networks, consisting of multiple light-emitting diodes (LEDs) acting as optical access points (APs), can provide low-cost high-rate data transmission to multiple users simultaneously in indoor environments. However, the performance of VLC networks is severely limited by the interference between different users. In this paper, we establish a distributed user-centric scheduling framework based on stable marriage theory, and propose a novel decentralized scheduling method to manage interference by forming flexible amorphous cells for all users. The proposed scheduling method has provable low computational complexity and requires only the exchange of a few 1-bit messages between the APs and the users but not the feedback of the channel state information of the entire network. We further show that the proposed method can achieve both user-wise and system-wise optimality as well as a certain level of fairness. Simulation results indicate that our decentralized user-centric scheduling method outperforms existing centralized approaches in terms of throughput, fairness, and computational complexity.