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Literatura académica sobre el tema "Uniformly dense hypergraph"
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Artículos de revistas sobre el tema "Uniformly dense hypergraph"
Reiher, Christian. "Extremal problems in uniformly dense hypergraphs". European Journal of Combinatorics 88 (agosto de 2020): 103117. http://dx.doi.org/10.1016/j.ejc.2020.103117.
Texto completoReiher, Christian, Vojtěch Rödl y Mathias Schacht. "Hypergraphs with vanishing Turán density in uniformly dense hypergraphs". Journal of the London Mathematical Society 97, n.º 1 (8 de diciembre de 2017): 77–97. http://dx.doi.org/10.1112/jlms.12095.
Texto completoReiher, Christian, Vojtĕch Rödl y Mathias Schacht. "On a generalisation of Mantel’s Theorem to Uniformly Dense Hypergraphs". International Mathematics Research Notices 2018, n.º 16 (7 de marzo de 2017): 4899–941. http://dx.doi.org/10.1093/imrn/rnx017.
Texto completoZHAO, YUFEI. "An arithmetic transference proof of a relative Szemerédi theorem". Mathematical Proceedings of the Cambridge Philosophical Society 156, n.º 2 (14 de noviembre de 2013): 255–61. http://dx.doi.org/10.1017/s0305004113000662.
Texto completoTesis sobre el tema "Uniformly dense hypergraph"
Zhou, Wenling. "Embedding problems in uniformly dense hypergraphs". Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG092.
Texto completoGiven a k-graph (k-uniform hypergraph) F, the Turán density π(F) of F is the maximum density among all F-free k-graphs. Determining π(F) for a given k-graph F is a classical extremal problem. Given two k-graphs F and H, a perfect F-tiling (or F-factor) of H is a collection of vertex-disjoint copies of F in H that together cover all the vertices of H. Perfect tiling problems, as a strengthening of the Turán problem, aim to find extremal conditions on H which guarantee an F-factor, which also has a long and profound history. In this thesis, we use many powerful tools including the probabilistic method, hypergraph regularity method and absorbing method to study Turán densities and perfect tilings of given k-graphs F in uniformly dense hypergraphs. Unlike graphs, we all know that there are several non-equivalent notions of quai-randomness in k-graphs for k ≥ 3. Hence, our work also has several non-equivalent definitions of uniformly dense k-graphs. Roughly speaking, a k-graph H is (d, μ, ⋆)-dense means that it is d-dense and ⋆-quai-randomness for some small μ > 0 with respect to given random structures. Restricting to (d, μ, 1)-dense 3-graphs, the Turán density of a given 3-graph F is denoted by π1(F). Determining π1(F) was suggested by Erdős and Sós in the 1980s. In 2018, Reiher, Rödl and Schacht extended the concept of (d, μ, 1)-dense 3-graphs to (d, μ, k-2)-dense k-graphs for k ≥ 3, and they proposed the study of uniform Turán density πk-2(F) for a given k-graph F in (d, μ, k-2)-dense k-graphs. In particular, they showed that πk-2(•) “jumps” from 0 to at least k-to-the-minus-kth-power. In this thesis, we obtain a sufficient condition for 3-graphs F which satisfy π1(F)= 1/4. Interestingly, currently all known 3-graphs F whose π1(F) is 1/4 satisfy this condition. In addition, we also construct some intriguing 3-graphs F with π1(F) = 1/4. For k-graphs, we give a framework to study πk-2(F) for any k-graph F. By using this framework, we give a sufficient condition for k-graphs F satisfying πk-2(F) is k-to-the-minus-kth-power, and construct an infinite family of k-graphs with πk-2(F) is k-to-the-minus-kth-power.In 2016, Lenz and Mubayi posed the problem of characterizing the k-graphs F such that every sufficiently large (d, μ, dot)-dense k-graph H with d > 0, v(F)|v(H) and positive minimum vertex degree contains an F-factor. Motivated by this problem, we prove a general theorem on F-factors which reduces the F-factors problem of Lenz and Mubayi to a natural sub-problem, that is, the F-cover problem. By using this result, we answer the question of Lenz and Mubayi for those F which are k-partite k-graphs and for all 3-graphs F, separately. In the work of Lenz and Mubayi, they also constructed a sequence of (1/8, μ, dot)-dense 3-graphs with positive minimum vertex degree having no F-factor, where F is a balanced complete 3-partite 3-graph. In this thesis, we prove that 1/8 is the density threshold for ensuring all 3-partite 3-graphs perfect tilings in (d, μ, dot)-dense 3-graphs given a minimum codegree condition Ω(n). Moreover, we show that one can not replace the minimum codegree condition with a minimum vertex degree condition. In particular, we study the optimal density threshold of F-factors for each 3-partite 3-graph F in (d, μ, dot)-dense 3-graphs with minimum codegree Ω(n). In addition, we also study F-factor problems for k-partite k-graphs F with stronger quasi-random assumption and positive minimum 1-degree