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.

In this version we have improved the running time from $O(c^m\cdot n^2)$ to $O(c^m\cdot n)$. To incorporate this, we had to apply some minor changes, mostly in Section 2, leaving the overall approach essentially unaffected. 10 pages