Classification of OBDD size for monotone 2-CNFs
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We introduce a new graph parameter called linear upper maximum induced matching width lu-mim width, denoted for a graph G by lu(G). We prove that the smallest size of the obdd for φ, the monotone 2-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.
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