De Bruijn graphs and DNA graphs

In this paper we prove the NP-hardness of various recognition problems for subgraphs of De Bruijn graphs. In particular, the recognition of DNA graphs is shown to be NP-hard; DNA graphs are the vertex induced subgraphs of De Bruijn graphs over a four letter alphabet. As a consequence, two open questions from a recent paper by Błażewicz, Hertz, Kobler & de Werra [Discrete Applied Mathematics 98, 1999] are answered in the negative