Clause-connected versions of the satisfiability problem

The satisfiability problem is one of the most famous computationally hard algorithmic problems. It is well known that the satisfiability problem remains hard even in the restricted version in which Boolean formulas in conjunctive normal form with exactly three distinct literals per clause. However, the problem can be solved in polynomial time for Boolean formulas with exactly two distinct literals per clause. Narrowing the gap between the problems is of fundamental interest. Therefore, it is natural to analyze the complexity of some restricted versions of the satisfiability problem. In this paper, we prove hardness of some clause-connected versions of the satisfiability problem.