  We introduce a new graph parameter called linear upper maximum induced
matching width \textsc{lu-mim width}, denoted for a graph $G$ by $lu(G)$. We
prove that the smallest size of the \textsc{obdd} for $\varphi$, the monotone
2-\textsc{cnf} corresponding to $G$, is sandwiched between $2^{lu(G)}$ and
$n^{O(lu(G))}$. The upper bound is based on a combinatorial statement that
might be of an independent interest. We show that the bounds in terms of this
parameter are best possible.
