Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
A short proof of Fisher's inequality
Discrete Mathematics
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
An O (N2.5) algorithm for maximum matching in general graphs
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
NP-Completeness of (k-SAT,r-UNk-SAT) and (LSAT ≥ k,r-UNLSAT ≥ k)
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
The existence of unsatisfiable formulas in k-LCNF for k ≥ 3
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A CNF class generalizing exact linear formulas
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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In the present paper we introduce the class of linear CNF formulas generalizing the notion of linear hypergraphs. Clauses of a linear formula intersect in at most one variable. We show that SAT for the general class of linear formulas remains NP-complete. Moreover we show that the subclass of exactly linear formulas is always satisfiable. We further consider the class of uniform linear formulas and investigate conditions for the formula graph to be complete. We define a formula hierarchy such that one can construct a 3-uniform linear formula belonging to the ith level such that the clause-variable density is of Ω(2.5i−−1) ∩O(3.2i−−1). Finally, we introduce the subclasses LCNF≥k of linear formulas having only clauses of length at least k, and show that SAT remains NP-complete for LCNF≥3.