The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and the fast-mixed searching, which implies some NP-completeness results for the zero forcing problem. For chordal graphs much is understood regarding the relat...

The zero forcing number is a graph invariant introduced in order to study the minimum rank of the graph. In the first part of this paper, we first highlight that the computation of the zero forcing number of any directed graph (allowing loops) is NP-hard. Furthermore, we identify a class of directed trees for which the zero forcing number is computable in linear time. The second part of the pap...

The zero forcing number is a graph invariant introduced in order to study the minimum rank of the graph. In the first part of this paper, we first highlight that the computation of the zero forcing number of any directed graph (allowing loops) is NP-hard. Furthermore, we identify a class of directed trees for which the zero forcing number is computable in linear time. The second part of the pap...

A certain approach to paraconsistency was initiated by works of R. Jennings and P. Schotch. In their “Inference and necessity” [4] they proposed a notion of a level of inconsistency (incoherence) of a given set of premises. This level is a measure that assigns to a given set of premises X, the least number of elements of covers of X that consist of consistent subsets of X. The idea of the level...

We will show that every subforcing of the basic Prikry forcing is either trivial or isomorphic to the Prikry forcing with the same ultrafilter. Let κ be a measurable cardinal and U a normal ultrafilter over κ. We will denote by P (U) the basic Prikry forcing with U . Let us recall the definition. Definition 0.1 P (U) is the set of all pairs 〈p,A〉 such that 1. p is a finite subset of κ, 2. A ∈ U...

Our aim is to define a version of a simpler short extenders forcing preserving strong cardinals. 1 The Main Preparation Forcing In this section we will redefine the preparation forcing of [6] in order to allow eventually to preserve strong cardinals. The definition will follow those of [6] with certain additions. Fix two cardinals κ and θ such that κ < θ and θ is regular. Definition 1.1 The set...

This paper addresses the problem of finding minimum forcing sets in origami. The origami material folds flat along straight lines called creases that can be labeled as mountains or valleys. A forcing set is a subset of creases that force all the other creases to fold according to their labels. The result is a flat folding of the origami material. In this paper we develop a linear time algorithm...

This paper addresses the problem of finding minimum forcing sets in origami. The origami material folds flat along straight lines called creases that can be labeled as mountains or valleys. A forcing set is a subset of creases that force all the other creases to fold according to their labels. The result is a flat folding of the origami material. In this paper we develop a linear time algorithm...