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 $\mathrm{\Delta }$ one can compute the number of subsets $S$ of $V(G)$ that induces a graph isomorphic to $H$in time $O(c^m\cdot n)$ for some constant $c=c(\mathrm{\Delta })>0$. This is essentially best possible.