Combinatorial Results on Directed Hypergraphs for the SAT Problem

Directed domination in oriented hypergraphs

ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...

Hypergraph Acyclicity and Propositional Model Counting

We show that the propositional model counting problem #SAT for CNFformulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #SAT was known to be solvable in polynomial time so far. Furthermore,...

Linear CNF formulas and satisfiability

In this paper, we study linear CNF formulas generalizing linear hypergraphs un-der combinatorial and complexity theoretical aspects w.r.t. SAT. We establish NP-completeness of SAT for the unrestricted linear formula class, and we show the equiv-alence of NP-completeness of restricted uniform linear formula classes w.r.t. SATand the existence of unsatisfiable uniform linear witne...

Max Horn Sat and Directed Hypergraphs: Algorithmic Enhancements and Easy Cases

On the orientation of graphs and hypergraphs

Graph orientation is a well-studied area of combinatorial optimization, one that provides a link between directed and undirected graphs. An important class of questions that arise in this area concerns orientations with connectivity requirements. In this paper we focus on how similar questions can be asked about hypergraphs, and we show that often the answers are also similar: many known graph ...