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Creators/Authors contains: "Rödl, Vojtech"

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  1. ; ; (, Combinatorics, Probability and Computing)
    Abstract Daisies are a special type of hypergraph introduced by Bollobás, Leader and Malvenuto. An$$r$$-daisy determined by a pair of disjoint sets$$K$$and$$M$$is the$$(r+|K|)$$-uniform hypergraph$$\{K\cup P\,{:}\, P\in M^{(r)}\}$$. Bollobás, Leader and Malvenuto initiated the study of Turán type density problems for daisies. This paper deals with Ramsey numbers of daisies, which are natural generalisations of classical Ramsey numbers. We discuss upper and lower bounds for the Ramsey number of$$r$$-daisies and also for special cases where the size of the kernel is bounded. 
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  2. ; (, Journal of Graph Theory)
    Abstract For a ‐uniform hypergraph we consider the parameter , the minimum size of a clique cover of the edge set of . We derive bounds on for belonging to various classes of hypergraphs. 
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  3. ; ; (, Journal of the London Mathematical Society)
    Accepted Manuscript Full Text Available
  4. ; (, Combinatorics, Probability and Computing)
    Abstract Let $$\mathrm{AP}_k=\{a,a+d,\ldots,a+(k-1)d\}$$ be an arithmetic progression. For $$\varepsilon>0$$ we call a set $$\mathrm{AP}_k(\varepsilon)=\{x_0,\ldots,x_{k-1}\}$$ an $$\varepsilon$$ -approximate arithmetic progression if for some a and d , $$|x_i-(a+id)|<\varepsilon d$$ holds for all $$i\in\{0,1\ldots,k-1\}$$ . Complementing earlier results of Dumitrescu (2011, J. Comput. Geom. 2 (1) 16–29), in this paper we study numerical aspects of Van der Waerden, Szemerédi and Furstenberg–Katznelson like results in which arithmetic progressions and their higher dimensional extensions are replaced by their $$\varepsilon$$ -approximation. 
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