The number of maximal independent sets in a connected graph
Discrete Mathematics
On generating all maximal independent sets
Information Processing Letters
Information Processing Letters
Acta Informatica
The number of maximal independent sets in triangle-free graphs
SIAM Journal on Discrete Mathematics
Maximal independent sets in graphs with at most one cycle
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parameterized Complexity
Annals of Mathematics and Artificial Intelligence
Satisfiability of mixed Horn formulas
Discrete Applied Mathematics
Algorithms for variable-weighted 2-SAT and dual problems
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
A new bound for an NP-hard subclass of 3-SAT using backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Simple but hard mixed horn formulas
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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We consider the satisfiability problem for CNF formulas that contain a (hidden) Horn and a 2-CNF (also called quadratic) part, called mixed (hidden) Horn formulas. We show that SAT remains NP-complete for such instances and also that any SAT instance can be encoded in terms of a mixed Horn formula in polynomial time. Further, we provide an exact deterministic algorithm showing that SAT for mixed (hidden) Horn formulas containing n variables is solvable in time O(2$^{\rm 0.5284{\it n}}$). A strong argument showing that it is hard to improve a time bound of O(2n/2) for mixed Horn formulas is provided. We also obtain a fixed-parameter tractability classification for SAT restricted to mixed Horn formulas C of at most k variables in its positive 2-CNF part providing the bound O(||C||20.5284k). Motivating examples for mixed Horn formulas are level graph formulas [14] and graph colorability formulas.