Abstract Let be a hypergraph, where is a set of vertices and is a set of clusters , , such that the clusters in are not necessarily disjoint. This article considers the feasibility clustered traveling salesman problem, denoted by . In the we aim to decide whether a simple path exists that visits each vertex exactly once, such that the vertices of each cluster are visited consecutively. We focus on hypergraphs with no feasible solution path and consider removing vertices from clusters, such that the hypergraph with the new clusters has a feasible solution path for . The algorithm uses a PQ‐tree data structure and runs in linear time.