MotifCut: regulatory motifs finding with maximum density subgraphs. Results: We present MotifCut, a graph-theoretic approach to motif finding leading to a convex optimization problem with a polynomial time solution. We build a graph where the vertices represent all k-mers in the input sequences, and edges represent pairwise k-mer similarity. In this graph, we search for a motif as the maximum density subgraph, which is a set of k-mers that exhibit a large number of pairwise similarities. Our formulation does not make strong assumptions regarding the structure of the motif and in practice both motifs that fit well the PSSM model, and those that exhibit strong dependencies between position pairs are found as dense subgraphs. We benchmark MotifCut on both synthetic and real yeast motifs, and find that it compares favorably to existing popular methods. The ability of MotifCut to detect motifs appears to scale well with increasing input size. Moreover, the motifs we discover are different from those discovered by the other methods. Availability: MotifCut server and other materials can be found at