Relevant bibliographies by topics / Hypergraph regularity lemma

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Hypergraph regularity lemma'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Hypergraph regularity lemma"

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Nagle, Brendan, Vojtěch Rödl, and Mathias Schacht. "An algorithmic hypergraph regularity lemma." Random Structures & Algorithms 52, no. 2 (2017): 301–53. http://dx.doi.org/10.1002/rsa.20739.

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CUTLER, JONATHAN, and A. J. RADCLIFFE. "Hypergraph Independent Sets." Combinatorics, Probability and Computing 22, no. 1 (2012): 9–20. http://dx.doi.org/10.1017/s0963548312000454.

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The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. There are a variety of types of independent sets in hypergraphs depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices isj-independentif its intersection with any edge has size strictly less thanj. The Kruskal–Katona theorem implies that in anr-uniform hypergraph with a fixed size and order, the hypergraph with the mostr-independent sets is the lexicographic hypergraph. In this paper, we use a hypergraph regularity le
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HAXELL, P. E., T. ŁUCZAK, Y. PENG, V. RÖDL, A. RUCIŃSKI, and J. SKOKAN. "The Ramsey Number for 3-Uniform Tight Hypergraph Cycles." Combinatorics, Probability and Computing 18, no. 1-2 (2009): 165–203. http://dx.doi.org/10.1017/s096354830800967x.

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LetC(3)ndenote the 3-uniformtight cycle, that is, the hypergraph with verticesv1, .–.–.,vnand edgesv1v2v3,v2v3v4, .–.–.,vn−1vnv1,vnv1v2. We prove that the smallest integerN=N(n) for which every red–blue colouring of the edges of the complete 3-uniform hypergraph withNvertices contains a monochromatic copy ofC(3)nis asymptotically equal to 4n/3 ifnis divisible by 3, and 2notherwise. The proof uses the regularity lemma for hypergraphs of Frankl and Rödl.
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Lyall, Neil, and Ákos Magyar. "Weak hypergraph regularity and applications to geometric Ramsey theory." Transactions of the American Mathematical Society, Series B 9, no. 5 (2022): 160–207. http://dx.doi.org/10.1090/btran/61.

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Let Δ = Δ 1 × … × Δ d ⊆ R n \Delta =\Delta _1\times \ldots \times \Delta _d\subseteq \mathbb {R}^n , where R n = R n 1 × ⋯ × R n d \mathbb {R}^n=\mathbb {R}^{n_1}\times \cdots \times \mathbb {R}^{n_d} with each Δ i ⊆ R n i \Delta _i\subseteq \mathbb {R}^{n_i} a non-degenerate simplex of n i n_i points. We prove that any set S ⊆ R n S\subseteq \mathbb {R}^n , with n = n 1 + ⋯ + n d n=n_1+\cdots +n_d of positive upper Banach density necessarily contains an isometric copy of all sufficiently large dilates of the configuration Δ \Delta . In particular any such set S ⊆ R 2 d S\subseteq \mathbb {R}^
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KRIVELEVICH, MICHAEL, MATTHEW KWAN, and BENNY SUDAKOV. "Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs." Combinatorics, Probability and Computing 25, no. 6 (2016): 909–27. http://dx.doi.org/10.1017/s0963548316000079.

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We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation. First, we prove that adding linearly many random edges to a densek-uniform hypergraph ensures the (asymptotically almost sure) existence of a perfect matching or a loose Hamilton cycle. The proof involves an interesting application of Szemerédi's Regularity Lemma, which might be independently useful. We next prove that digraphs with certain strong expansion properties are pancyclic, and use this to show that adding
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RÖDL, VOJTĚCH, and MATHIAS SCHACHT. "Regular Partitions of Hypergraphs: Regularity Lemmas." Combinatorics, Probability and Computing 16, no. 6 (2007): 833–85. http://dx.doi.org/10.1017/s0963548307008553.

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Szemerédi's regularity lemma for graphs has proved to be a powerful tool with many subsequent applications. The objective of this paper is to extend the techniques developed by Nagle, Skokan, and the authors and obtain a stronger and more ‘user-friendly’ regularity lemma for hypergraphs.
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RÖDL, VOJTĚCH, and MATHIAS SCHACHT. "Regular Partitions of Hypergraphs: Counting Lemmas." Combinatorics, Probability and Computing 16, no. 6 (2007): 887–901. http://dx.doi.org/10.1017/s0963548307008565.

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We continue the study of regular partitions of hypergraphs. In particular, we obtain corresponding counting lemmas for the regularity lemmas for hypergraphs from our paper ‘Regular Partitions of Hypergraphs: Regularity Lemmas’ (in this issue).
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Czygrinow, Andrzej, and Vojtech Rödl. "An Algorithmic Regularity Lemma for Hypergraphs." SIAM Journal on Computing 30, no. 4 (2000): 1041–66. http://dx.doi.org/10.1137/s0097539799351729.

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Rödl, Vojtěch, and Jozef Skokan. "Regularity Lemma for k-uniform hypergraphs." Random Structures & Algorithms 25, no. 1 (2004): 1–42. http://dx.doi.org/10.1002/rsa.20017.

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Rödl, Vojtěch, and Jozef Skokan. "Applications of the regularity lemma for uniform hypergraphs." Random Structures and Algorithms 28, no. 2 (2006): 180–94. http://dx.doi.org/10.1002/rsa.20108.

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Dissertations / Theses on the topic "Hypergraph regularity lemma"

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Khan, Shoaib Amjad. "A hypergraph regularity method for linear hypergraphs." [Tampa, Fla] : University of South Florida, 2009. http://purl.fcla.edu/usf/dc/et/SFE0003001.

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Hàn, Hiêp. "Extremal hypergraph theory and algorithmic regularity lemma for sparse graphs." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16402.

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Einst als Hilfssatz für Szemerédis Theorem entwickelt, hat sich das Regularitätslemma in den vergangenen drei Jahrzehnten als eines der wichtigsten Werkzeuge der Graphentheorie etabliert. Im Wesentlichen hat das Lemma zum Inhalt, dass dichte Graphen durch eine konstante Anzahl quasizufälliger, bipartiter Graphen approximiert werden können, wodurch zwischen deterministischen und zufälligen Graphen eine Brücke geschlagen wird. Da letztere viel einfacher zu handhaben sind, stellt diese Verbindung oftmals eine wertvolle Zusatzinformation dar. Vom Regularitätslemma ausgehend gliedert sich
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Yilma, Zelealem Belaineh. "Results in Extremal Graph and Hypergraph Theory." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/49.

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In graph theory, as in many fields of mathematics, one is often interested in finding the maxima or minima of certain functions and identifying the points of optimality. We consider a variety of functions on graphs and hypegraphs and determine the structures that optimize them. A central problem in extremal (hyper)graph theory is that of finding the maximum number of edges in a (hyper)graph that does not contain a specified forbidden substructure. Given an integer n, we consider hypergraphs on n vertices that do not contain a strong simplex, a structure closely related to and containing a simp
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Zhou, Wenling. "Embedding problems in uniformly dense hypergraphs." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG092.

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Étant donné un k-graph (hypergraphe k-uniforme) F, la densité de Turán π(F) de F est la densité maximale parmi tous les k-graphes F-libres. Déterminer π(F) pour un k-graph donné F est un problème extrémal classique. Étant donnés deux k-graphes F et H, un F-facteur de H est une collection de copies de F disjointes sur les sommets de H qui couvrent ensemble tous les sommets de H. Les problèmes de F-facteurs, en tant que renforcement du problème de Turán, visent à trouver des conditions extrémales sur H garantissant un F-facteur, ce qui a également une histoire longue et profonde. Dans cette thès
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Hạ̀n, Hiêp [Verfasser], Mihyun Akademischer Betreuer] Kang, Anusch [Akademischer Betreuer] [Taraz та Hanno [Akademischer Betreuer] Lefmann. "Extremal hypergraph theory and algorithmic regularity lemma for sparse graphs / Hiêp Hạ̀n. Gutachter: Mihyun Kang ; Anuschirawan Taraz ; Hanno Lefmann". Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://d-nb.info/1017495084/34.

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Schacht, Mathias. "Regular partitions of hypergraphs and property testing." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2010. http://dx.doi.org/10.18452/13975.

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Die Regularitätsmethode für Graphen wurde vor über 30 Jahren von Szemerédi, für den Beweis seines Dichteresultates über Teilmengen der natürlichen Zahlen, welche keine arithmetischen Progressionen enthalten, entwickelt. Grob gesprochen besagt das Regularitätslemma, dass die Knotenmenge eines beliebigen Graphen in konstant viele Klassen so zerlegt werden kann, dass fast alle induzierten bipartiten Graphen quasi-zufällig sind, d.h. sie verhalten sich wie zufällige bipartite Graphen mit derselben Dichte. Das Regularitätslemma hatte viele weitere Anwendungen, vor allem in der extremalen Gr
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Person, Yury. "Quasi-random hypergraphs and extremal problems for hypergraphs." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2010. http://dx.doi.org/10.18452/16238.

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In dieser Arbeit wird zuerst das Theorem von Chung, Graham und Wilson über quasi-zufällige Graphen zur sogenannten schwachen Quasi-Zufälligkeit für k-uniforme Hypergraphen verallgemeinert und somit eine Reihe äquivalenter Eigenschaften bestimmt. Basierend auf diesen Resultaten werden nichtbipartite Graphen gefunden, welche die Quasi-Zufälligkeit für Graphen ``forcieren''''. Zuvor waren nur bipartite Graphen mit dieser Eigenschaft bekannt. Desweiteren ist ein konzeptionell einfacher Algorithmus zum Verifizieren nicht erfüllbarer zufälliger k-SAT Formeln angegeben. Dann richtet sich der Fok
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Book chapters on the topic "Hypergraph regularity lemma"

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Szemerédi, Endre. "Various Regularity Lemmas in Graphs and Hypergraphs." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-39053-1_47.

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Conference papers on the topic "Hypergraph regularity lemma"

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Nagle, Brendan, Vojtěch Rödl, and Mathias Schacht. "An Algorithmic Hypergraph Regularity Lemma." In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2015. http://dx.doi.org/10.1137/1.9781611974331.ch122.

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