In the Minimum k‐Path Connected Vertex Cover Problem (MkPCVCP), we are given a connected graph G and an integer k ≥ 2, and are required to find a subset C of vertices with minimum cardinality such that each path with length k − 1 has a vertex in C, and moreover, the induced subgraph G[C] is connected. MkPCVCP is a generalization of the minimum connected vertex cover problem and has applications in many areas such as security communications in wireless sensor networks. MkPCVCP is proved to be NP‐complete. In this paper, we give the first polynomial time approximation scheme (PTAS) for MkPCVCP in unit disk graphs, for every fixed k ≥ 2.
