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For a graph G, a function \(\psi \) is called a bar visibility representation of G when for each vertex \(v \in V(G)\), \(\psi (v)\) is a horizontal line segment (bar) and \(uv \in E(G)\) if and only if there is an unobstructed, vertical, \(\varepsilon \)-wide line of sight between \(\psi (u)\) and \(\psi (v)\). Graphs admitting such representations are well understood (via...

& **Tomasz** **Krawczyk**
A series of tetraalkylammonium catalysts immobilized on polystyrene or carbon nanotubes were investigated in a reaction between alkyl halides, amines, and CO2. The yield of carbamates was

**Tomasz** **Krawczyk**
Arkadiusz Pawlik
Bartosz Walczak
Recently, it was proved that triangle-free intersection graphs of n line segments in the plane can have chromatic number as large as ( log log n

Background Adhesive molecules like CD44 are well defined key players in the metastatic cascade in many cancers, including endometrial cancer. They could play a role of markers of invasion, metastasis and prognostic factors. Aim of the study The aim of the study is to assess a possible role of the CD44 as a marker of invasion in endometrial cancer, both at the moment of...

We analyze the on-line dimension of partially ordered sets as a value of a two-person game between Algorithm and Spoiler. The game is played in rounds. Spoiler presents an on-line order of width at most w, one point at a time. Algorithm maintains its realizer, i.e., the set of d linear extensions which intersect to the presented order. Algorithm may not change the ordering of the...

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set \(X\) in \(\mathbb{R }^2\) that is not an...