  We introduce a new graph parameter called linear upper maximum induced
matching 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.
