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The Uniformity Lemma for hypergraphs
Graphs and Combinatorics, 1992This is an extension of Szemerédi's theorem called the Uniformity Lemma for Graphs (see \textit{E. Szemerédi} [Problèmes combinatoires et théorie des graphes, Orsay 1976, Colloq. int. CNRS No. 260, 399-401 (1978; Zbl 0413.05055)]) to \(r\)-uniform hypergraphs. Two applications of the result are announced: proof of a conjecture of Erdős concerning Turán-
Frankl, Peter, Rödl, Vojtěch
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Relative Turán Problems for Uniform Hypergraphs
SIAM Journal on Discrete Mathematics, 202122 ...
Spiro, Sam, Verstraëte, Jacques
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Realizing an m-Uniform Four-Chromatic Hypergraph with Disks
Combinatorica, 2020We prove that for every positive integer m there is a finite point set P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Gábor Damásdi, Dömötör Pálvölgyi
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Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs
Symposium on Theoretical Aspects of Computer Science, 2023A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, …, k such that each edge contains a unique maximal colour.
Marek Filakovský +4 more
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2-Colorings of uniform hypergraphs
Mathematical Notes, 2016One of the most popular and classical extremal problems in hypergraph theory is the property of the existence \(2\)-coloring of its vertex set such that no hyper-edge of the hypergraph concerned is monochromatic. Certain bounds for the least number \(m(n)\) of edges of an \(n\)-uniform hypergraph with this property have been determined in the recent ...
Demidovich, Yu. A., Raigorodskii, A. M.
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Hypergraph: A Unified and Uniform Definition with Application to Chemical Hypergraph
arXiv.orgThe conventional definition of hypergraph has two major issues: (1) there is not a standard definition of directed hypergraph and (2) there is not a formal definition of nested hypergraph.
Daniel T. Chang
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Self-Complementary Non-Uniform Hypergraphs
Graphs and Combinatorics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Intersection Multigraphs of Uniform Hypergraphs
Graphs and Combinatorics, 1998A hypergraph \(H=(V,\{X_i \mid i\in I\})\) is \(k\)-uniform if all hyperedges \(X_i\) have the same cardinality \(k\); it is \(k\)-conformal if there is some graph \(G\) such that \(H\) is isomorphic to the hypergraph of all cliques with \(k\) vertices of \(G\).
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Partitioning dense uniform hypergraphs
Journal of Combinatorial Optimization, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Shufei, Hou, Jianfeng
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Regularity Lemma for k‐uniform hypergraphs
Random Structures & Algorithms, 2004AbstractSzemerédi's Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi‐randomness, Random Structures Algorithms 2 (1991), 241–252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs Combin 8 (1992), 309–312; Extremal problems on ...
Rödl, Vojtěch, Skokan, Jozef
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