With the low latency and high coverage, the low earth orbit (LEO) satellite systems are attracting more and more venture capitals as well as research attentions. Due to their highly dynamic constellation topologies, routing protocols on the ground have to be tailored to efficiently adapt to the regular topology changes. However, for irregular topology changes caused by exceptional link failure/recovery, network-wide route flooding is still necessary for route convergence. But, this will cause significant traffic flooding redundancy due to the high density of constellation topologies. For larger-scale constellations, the redundancy issue will be exacerbated. To lessen the redundancy, this work proposes a lightweight route flooding mechanism by generating a sparse flooding topology that prunes the original full-mesh topology, and only flooding the route information on the sparse topology. By considering the maximum flooding hop as well as the robustness of the flooding topology, we design an algorithm to calculate the optimal topology instead of just applying the minimum spanning tree. The evaluation shows that, for the LEO-96 constellation, the new flooding topology has a 28.1% reduction in the inter-satellite links (ISLs) compared with the original topology, and the new flooding mechanism has a 37.52% reduction in the traffic flooded and a 10.03% reduction in the route convergence time compared with OSPF. Such improvements will be amplified on larger-scale constellations.