In multi-unmanned aerial vehicle (multi-UAV) cooperative search missions, to address the issue of reduced collaborative search efficiency due to poor electromagnetic environments, a communication topology model based on the minimum spanning tree is established by considering communication range and cluster communication topology structure. On this model, search performance metrics are designed, and these metrics are optimized using a distributed receding horizon framework. Simulation results show that the minimum spanning tree communication topology improves search efficiency by 23.1% compared to fully connected communication topology, fully utilizing the resource advantages of UAV clusters, overcoming issues such as reduced reliable communication range and non-complete connectivity of communication topology, thereby enhancing the adaptability of UAV cluster cooperative search algorithms to communication-constrained environments.