Related papers: Hypergraphs and proper forcing

In this paper, we characterize chordal and perfect zero-divisor graphs of finite posets. Also, it is proved that the zero-divisor graphs of finite posets and the complement of zero-divisor graphs of finite $0$-distributive posets satisfy…

We introduce a new topological generalization of the $\sigma$-projective hierarchy, not limited to Polish spaces. Earlier attempts have replaced $^{\omega}\omega$ by $^{\kappa}\kappa$, for $\kappa$ regular uncountable, or replaced countable…

We describe a method of building ``nice'' sigma-ideals from Souslin ccc forcing notions. [These notes were written down in 1992, but were not submitted to any journal. In a slightly modified form, they were incorporated to: T. Bartoszynski…

Hypergraphic polytopes $\Delta_{\mathbb{H}}$ arise as Minkowski sums of simplices indexed by the hyperedges of a hypergraph $\mathbb{H}$. Orienting the $1$-skeleton of such a polytope by a certain generic linear functional gives rise to the…

Let G be a graph with a perfect matching. A complete forcing set of G is a subset of edges of G to which the restriction of every perfect matching is a forcing set of it. The complete forcing number of G is the minimum cardinality of…

A quotient of a poset $P$ is a partial order obtained on the equivalence classes of an equivalence relation $\theta$ on $P$; $\theta$ is then called a congruence if it satisfies certain conditions, which vary according to different…

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a…

Several recent papers have explored families of rational polyhedra whose integer points are in bijection with certain families of numerical semigroups. One such family, first introduced by Kunz, has integer points in bijection with…

We use coherent systems of FS iterations on a power set, which can be seen as matrix iteration that allows restriction on arbitrary subsets of the vertical component, to prove general theorems about preservation of certain type of unbounded…

In this paper we consider a notion of universal sets for ideals. We show that there exist universal sets of minimal Borel complexity for classic ideals like null subsets of $2^\omega$ and meager subsets of any Polish space, and demonstrate…

We show that posets of bounded height whose cover graphs exclude a fixed graph as a topological minor have bounded dimension. This result was already proven by Walczak. However, our argument is entirely combinatorial and does not rely on…

For an $n$-vertex graph $G$, let $z(G;k)$ denote the number of zero forcing sets of size $k$. A conjecture of Boyer et al. asserts that the path $P_n$ maximizes these numbers coefficientwise among all $n$-vertex graphs; equivalently, the…

In this paper, our main focus is to explore different classes of nearly normally torsion-free ideals. We first characterize all finite simple connected graphs with nearly normally torsion-free cover ideals. Next, we characterize all…

In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…

We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequence on $\omega_2$ using finite conditions.

In this paper we show that forcings which are strongly proper for stationarily many countable elementary submodels preserve each of the following properties of topological spaces: countably tight; Lindel\"of; Rothberger; Menger; and a…

Zero forcing is an iterative coloring process on a graph that has been widely used in such different areas as the modelling of propagation phenomena in networks and the study of minimum rank problems in matrices and graphs. This paper deals…

In this paper, we introduce the notion of the containment graph of a family of sets and containment classes of graphs and posets. Let $Z$ be a family of nonempty sets. We call a (simple, finite) graph G = (V, E) a $Z$-containment graph…

An action on order ideals of posets considered by Fon-Der-Flaass is analyzed in the case of posets arising from minuscule representations of complex simple Lie algebras. For these minuscule posets, it is shown that the Fon-Der-Flaass action…

We compute the characteristic polynomials of the posets of hypertrees. We show that the generating series of the polynomials can be expressed using cyclic hypertrees. We also propose a conjecture on the action of the symmetric groups on the…