Embedding and Ramsey numbers of sparse \(k\)-uniform hypergraphs

DOI10.1007/s00493-009-2356-yzbMath1212.05170arXivmath/0612351OpenAlexW2022230023MaRDI QIDQ987557

Oliver Cooley, Deryk Osthus, Daniela Kühn, Nikolaos Fountoulakis

Publication date: 13 August 2010

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612351

zbMATH Keywords

hypergraphsRamsey numbers

Mathematics Subject Classification ID

Hypergraphs (05C65) Generalized Ramsey theory (05C55)

Related Items (23)

Hamilton \(\ell\)-cycles in randomly perturbed hypergraphs ⋮ Regular slices for hypergraphs ⋮ Boolean lattices: Ramsey properties and embeddings ⋮ On two problems in graph Ramsey theory ⋮ Ramsey numbers of 3-uniform loose paths and loose cycles ⋮ Diagonal Ramsey Numbers of Loose Cycles in Uniform Hypergraphs ⋮ Monochromatic loose-cycle partitions in hypergraphs ⋮ Large Yk,b ${Y}_{k,b}$‐tilings and Hamilton ℓ $\ell $‐cycles in k $k$‐uniform hypergraphs ⋮ Minimum degree conditions for tight Hamilton cycles ⋮ F$F$‐factors in Quasi‐random Hypergraphs ⋮ Tiling multipartite hypergraphs in quasi-random hypergraphs ⋮ Covering and tiling hypergraphs with tight cycles ⋮ Monochromatic bounded degree subgraph partitions ⋮ Tight cycles and regular slices in dense hypergraphs ⋮ Hamilton \(\ell \)-cycles in uniform hypergraphs ⋮ Dependent random choice ⋮ Ramsey numbers of sparse hypergraphs ⋮ Ramsey numbers of sparse hypergraphs ⋮ The Ramsey number of Fano plane versus tight path ⋮ A hypergraph blow-up lemma ⋮ Partitioning Edge-Colored Hypergraphs into Few Monochromatic Tight Cycles ⋮ Minimum Vertex Degree Threshold for ‐tiling* ⋮ On Ordered Ramsey Numbers of Tripartite 3-Uniform Hypergraphs

Cites Work

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• Blow-up lemma
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• Hypergraph regularity and the multidimensional Szemerédi theorem
• 3-uniform hypergraphs of bounded degree have linear Ramsey numbers
• Short paths in quasi-random triple systems with sparse underlying graphs
• A hypergraph blow-up lemma
• Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
• Linear Ramsey Numbers for Bounded-Degree Hypergrahps
• The Ramsey Number for 3-Uniform Tight Hypergraph Cycles
• Regularity properties for triple systems
• On graphs with linear Ramsey numbers
• Extremal problems on set systems
• Regularity Lemma for k-uniform hypergraphs
• Regular Partitions of Hypergraphs: Regularity Lemmas
• Regular Partitions of Hypergraphs: Counting Lemmas
• The counting lemma for regular k‐uniform hypergraphs
• Combinatorial Theorems on Classifications of Subsets of a Given Set
• Ramsey numbers of sparse hypergraphs

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