The De Bruijn graph (DBG) has been widely used in the algorithms for indexing or organizing read and reference sequences in bioinformatics. However, a DBG model that can locate each node, edge and path on sequence has not been proposed so far. Recently, DBG has been used for representing reference sequences in read mapping tasks. In this process, it is not a one-to-one correspondence between the paths of DBG and the substrings of reference sequence. This results in the false path on DBG, which means no substrings of reference producing the path. Moreover, if a candidate path of a read is true, we need to locate it and verify the candidate on sequence. To solve these problems, we proposed a DBG model, called MiniDBG, which stores the position lists of a minimal set of edges. With the position lists, MiniDBG can locate any node, edge and path efficiently. We also proposed algorithms for generating MiniDBG based on an original DBG and algorithms for locating edges or paths on sequence. We designed and ran experiments on real datasets for comparing them with BWT-based and position list-based methods. The experimental results show that MiniDBG can locate the edges and paths efficiently with lower memory costs.