Computing the Number of Induced Copies of a Fixed Graph in a Bounded Degree Graph

In this paper we show that for any graph H of order m and any graph G of order n and maximum degree Delta one can compute the number of subsets S of V(G) that induces a graph isomorphic to H in time O(c(m).n) for some constant c = c(Delta) > 0. This is essentially best possible (in the sense that there is no c(o(m)) poly(n)-time algorithm under the exponential time hypothesis).