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We look at dynamic programming algorithms for propositional model counting, also called #SAT, and MaxSAT. Tools from graph structure theory, in particular treewidth, have been used to successfully identify tractable cases in many subfields of AI, including SAT, Constraint Satisfaction Problems (CSP), Bayesian reasoning, and planning. In this paper we attack #SAT and MaxSAT using similar, but more modern, graph structure tools. The tractable cases will include formulas whose class of incidencedoi:10.1613/jair.4831 fatcat:akaeiy75tbaibdntc7bwuojr44