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With the booming development of marine exploration technology, new studies such as the oceanix city, smart coastal city, and underwater smart cities have been proposed, and the Internet of Underwater Things (IoUT) has received a lot of attention. Data collection is an important application of the IoUT. The common method is to collect data by traversing the network using underwater intelligent devices, such as Autonomous Underwater Vehicles (AUVs). However, traditional data collection methods focus more on issues, such as path planning or the task assignment of AUVs. It is commonly known that the MAC protocol plays a crucial role in data transmission, which is designed to solve the competition issue for shared channels. However, the research on MAC is very challenging owing to the characteristics of hydroacoustic communication, e.g., the low bandwidth, high error rate, and long transmission latency. Hence, this paper proposes a MAC protocol based on an Interference Cancellation Graph (ICG-MAC) for AUV-assisted IoUT. It ensures that AUVs can join the network for data transmission immediately after arriving at the target area and they do not interfere with the normal work of other sensor nodes. Firstly, the target area to be reached by an AUV for data collection is defined according to the node degree and residual energy; then the interference model between neighboring nodes is analyzed and an Interference Cancellation Graphx is established, based on which the time slots are allocated for sensor nodes; and finally, the AUV moves to the target area for conflict-free data collection. The simulation results show that the proposed algorithm outperforms the comparison algorithms in terms of the network throughput and energy consumption. With the assistance of an AUV, better network connectivity and higher network traffic can be obtained.