  A vertex subset $S$ in a graph $G$ is a dominating set if every vertex not
contained in $S$ has a neighbor in $S$. A dominating set $S$ is a connected
dominating set if the subgraph $G[S]$ induced by $S$ is connected. A connected
dominating set $S$ is a minimal connected dominating set if no proper subset of
$S$ is also a connected dominating set. We prove that there exists a constant
$\varepsilon > 10^{-50}$ such that every graph $G$ on $n$ vertices has at most
$O(2^{(1-\varepsilon)n})$ minimal connected dominating sets. For the same
$\varepsilon$ we also give an algorithm with running time
$2^{(1-\varepsilon)n}\cdot n^{O(1)}$ to enumerate all minimal connected
dominating sets in an input graph $G$.
