This paper deals with the problem of additional sensor location in order to recover the observability of any given part of the state for structured linear systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. We first provide new graphical necessary and sufficient conditions for the generic partial observability. Then, we study the location of additional sensors in order to satisfy the latter conditions. We provide necessary and sufficient requirements to be satisfied by these additional sensors and all their possible locations. The proposed solution is simple to implement because it is based on well-known algorithms, usually used for finding successors and predecessors of vertex subsets or on computation of maximal linkings in a digraph. All the used algorithms have polynomial complexity orders. (C) 2013 Elsevier Ltd. All rights reserved.