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In natural images, object skeletons are used to represent geometric shapes. However, even slight variations in pose or movement can cause noticeable changes in skeleton structure, increasing the difficulty of detecting the skeleton and often resulting in discontinuous skeletons. Existing methods primarily focus on point-level skeleton point detection and overlook the importance of structural continuity in recovering complete skeletons. To address this issue, we propose Lighthouse-Skel, a topology-aware skeleton detection method via lighthouse-guided structured inference. Specifically, we introduce a dual-branch collaborative detection framework that jointly learns skeleton confidence field and structural anchors, including endpoints and junction points. The spatial distributions learned by the point branch guide the network to focus on topologically vulnerable regions, which improves the accuracy of skeleton detection. Based on the learned skeleton confidence field, we further propose a lighthouse-guided topology completion strategy, which uses detected junction points and breakpoints as lighthouses to reconnect discontinuous skeleton segments along low-cost paths, thereby improving skeleton continuity and structural integrity. Experimental results on four public datasets demonstrate that the proposed method achieves competitive detection accuracy while substantially improving skeleton connectivity and structural integrity.