The problem Max-Sat ask you to find an assignment of a CNF formula which satisfy as many clauses as possible.
For the simpler problem SAT there are many known special cases which can be solved in polynomial time, e.g. we can solve 2-SAT in polynomial time.
For Max-Sat the situation is different since Max-Sat is NP-hard even for 2-CNF formulas (each clause contains only 2 variables).
Is there any interesting special inputs for which Max-Sat is polynomial?
In particular I would be interested in a standard reference for solving Max-Sat when the incedence graph has bounded treewidth.