Computing the number of induced copies of a fixed graph in a bounded degree graph

Abstract: 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 $O(c^m\cdot n)$ for some constant $c = c(\Delta) > 0$. This is essentially best possible.