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Search: authors:"Tomasz Krawczyk"

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The Partial Visibility Representation Extension Problem

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...

Polymer- and Carbon Nanotube-Supported Heterogeneous Catalysts for the Synthesis of Carbamates from Halides, Amines, and CO2

& 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

CD44 expression in curettage and postoperative specimens of endometrial cancer

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...

Coloring Triangle-Free Rectangle Overlap Graphs with \(O(\log \log n)\) Colors

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

On-Line Dimension of Semi-Orders

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...

Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

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...