Trivial, Tractable, Hard. A Not So Sudden Complexity Jump in Neighborhood Restricted CNF Formulas

For a CNF formula F we define its 1-conflict graph as follows: Two clauses C,D ∈ F are connected by an edge if they have a nontrivial resolvent – that is, if there is a unique literal u ∈ C for which \(\bar{u} \in D\). Let lc1(F) denote the maximum degree of this graph.

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