
A generalization of the KőváriSósTurán theorem
We present a new proof of the KőváriSósTurán theorem that ex(n, K_s,t)...
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On Ramsey numbers of hedgehogs
The hedgehog H_t is a 3uniform hypergraph on vertices 1,...,t+t2 such t...
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A Separator Theorem for Hypergraphs and a CSPSAT Algorithm
We show that for every r ≥ 2 there exists ϵ_r > 0 such that any runifor...
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Dense Peelable Random Uniform Hypergraphs
We describe a new family of kuniform hypergraphs with independent rando...
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On the complexity of coloravoiding site and bond percolation
The mathematical analysis of robustness and errortolerance of complex n...
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Recurrently Predicting Hypergraphs
This work considers predicting the relational structure of a hypergraph ...
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EarSlicing for Matchings in Hypergraphs
We study when a given edge of a factorcritical graph is contained in a ...
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Connected Fair Detachments of Hypergraphs
Let 𝒢 be a hypergraph whose edges are colored. An (α,n)detachment of 𝒢 is a hypergraph obtained by splitting a vertex α into n vertices, say α_1,…,α_n, and sharing the incident hinges and edges among the subvertices. A detachment is fair if the degree of vertices and multiplicity of edges are shared as evenly as possible among the subvertices within the whole hypergraph as well as within each color class. In this paper we solve an open problem from 70s by finding necessary and sufficient conditions under which a kedgecolored hypergraph 𝒢 has a fair detachment in which each color class is connected. Previously, this was not even known for the case when 𝒢 is an arbitrary graph (i.e. 2uniform hypergraph). We exhibit the usefulness of our theorem by proving a variety of new results on hypergraph decompositions, and completing partial regular combinatorial structures.
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