How many conflicts does it need to be unsatisfiable?
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
The local lemma is tight for SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Constraint Satisfaction Problems in Clausal Form I: Autarkies and Deficiency
Fundamenta Informaticae
XSAT and NAE-SAT of linear CNF classes
Discrete Applied Mathematics
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The (k,s)-SAT problem is the satisfiability problem restricted to instances where each clause has exactly k literals and every variable occurs at most s times. It is known that there exists a function f such that for s \leq f(k) all (k,s)-SAT instances are satisfiable, but (k,f(k)+1)-SAT is already NP-complete (k \geq 3). We prove that f(k) = O(2k \cdot log k/k), improving upon the best known upper bound O(2k/kalpha), where alpha=log3 4 - 1 \approx 0.26. The new upper bound is tight up to a log k factor with the best known lower bound Omega(2k/k).