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A simple regularization of hypergraphs
"... Abstract. We give a simple and natural construction of hypergraph regularization. It yields a short proof of a hypergraph regularity lemma. Consequently, as an example of its applications, we have a short self-contained proof of Szemerédi’s classic theorem on arithmetic progressions (1975) as well a ..."
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Abstract. We give a simple and natural construction of hypergraph regularization. It yields a short proof of a hypergraph regularity lemma. Consequently, as an example of its applications, we have a short self-contained proof of Szemerédi’s classic theorem on arithmetic progressions (1975) as well as its multidimensional extension by Furstenberg-Katznelson (1978). 1.
unknown title
, 2007
"... Abstract. We show that the the Ramsey number of every bounded-degree uniform hypergraph is linear with respect to the number of vertices. This is a hypergraph extension of the famous theorem for ordinary graphs which Chvátal et al. [8] showed in 1983. Our result may demonstrate the potential of a ne ..."
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Abstract. We show that the the Ramsey number of every bounded-degree uniform hypergraph is linear with respect to the number of vertices. This is a hypergraph extension of the famous theorem for ordinary graphs which Chvátal et al. [8] showed in 1983. Our result may demonstrate the potential of a new hypergraph regularity lemma by [18]. 1.
