We show that all minimal dominating sets of a chordal bipartite graph can be generated in incremental polynomial, hence output polynomial, time. Enumeration of minimal dominating sets in graphs is equivalent to enumeration of minimal transversals in hypergraphs. Whether the minimal transversals of a hypergraph can be enumerated in output polynomial time is a well-studied and challenging questio...

We consider a generalization of the notion of transversal to a finite hypergraph, so called weighted transversals. Given a non-negative weight vector assigned to each hyperedge of an input hypergraph A and a nonnegative threshold vector, we define a weighted transversal as a minimal vertex set which intersects all the hyperedges of A except for a subfamily of total weight not exceeding the give...

We consider the problem of finding all minimal transversals of a hypergraph H ⊆ 2 , given by an explicit list of its hyperedges. We give a new decomposition technique for solving the problem with the following advantages: (i) Global parallelism: for certain classes of hypergraphs, e.g. hypergraphs of bounded edge size, and any given integer k, the algorithm outputs k minimal transversals of H i...

A perfect transversal of a graph is a set of vertices that meets any maximal clique, or any maximal stable set of the graph in exactly one vertex. In this paper we give some properties of perfect transversals in graph products. One of these properties is the characterization of the existence of perfect transversals in some graph products via perfect transversals of the factors. As an applicatio...

In this paper we study various predicates concerning line transversals to lines and segments in 3D. We compute the degrees of standard methods of evaluating these predicates. The degrees of some of these methods are surprisingly high, which may explain why computing line transversals with finite precision is prone to error. Our results suggest the need to explore alternatives to the standard me...

In this paper, we study some average properties of hypergraphs and the average complexity of algorithms applied to hypergraphs under different probabilistic models. Our approach is both theoretical and experimental since our goal is to obtain a random model that is able to capture the real-data complexity. Starting from a model that generalizes the Erdös-Renyi model [9, 10], we obtain asymptoti...