Jakub Cerný

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Let X be a set of points in general position in the plane. General position means that no three points lie on a line and no two points have the same x-coordinate. Y ⊆ X is a cup, resp. cap, if the points of Y lie on the graph of a convex, resp. concave function. Denote the points of Y by p1, p2, . . . , pm according to the increasing x-coordinate. The set Y(More)
For an integer <i>h</i> &#8805; 1, an <i>elementary h-route flow</i> is a flow along <i>h</i> edge disjoint paths between a source and a sink, each path carrying a unit of flow, and a single commodity <i>h-route flow</i> is a non-negative linear combination of elementary <i>h</i>-flows. An instance of a <i>single source multicommodity flow problem</i> for a(More)
The main objective of the study is investigation of mechanical properties of polyamide 6. These properties were examined in dependence on the dosage of the ionizing electron beam (beta) radiation and in dependence on the amount of cross-linking agent. Non-irradiated samples and those irradiated by dosage 66, 99 and 132 kGy were compared. Key-Words:(More)
AIM To provide an overview of gambling and associated problems in the Czech Republic, including an overview of the historical context, legislation, prevalence, treatment and research base and agenda. METHODS A review of literature and relevant sources. RESULTS The trajectory of gambling patterns in the territory of the Czech Republic in the 20th century(More)
We study the maximum possible number f(k, l) of intersections of the boundaries of a simple k-gon with a simple l-gon in the plane for k, l ≥ 3. To determine the number f(k, l) is quite easy and known when k or l is even but still remains open for k and l both odd. We improve (for k ≤ l) the easy upper bound kl − l to kl − ⌈k/6⌉ − l and obtain exact bounds(More)
We prove that the crossing number of a graph decays in a “continuous fashion” in the following sense. For any ε > 0 there is a δ > 0 such that for a sufficiently large n, every graph G with n vertices and m ≥ n edges, has a subgraph G of at most (1 − δ)m edges and crossing number at least (1 − ε)cr(G). This generalizes the result of J. Fox and Cs. Tóth.