, Volume 37, Issue 1, pp 31–40 | Cite as

Sparse hypergraphs with low independence number

Original Paper


Let K 4 (3) denote the complete 3-uniform hypergraph on 4 vertices. Ajtai, Erdős, Komlós, and Szemerédi (1981) asked if there is a function ω(d)→∞ such that every 3-uniform, K 4 (3) -free hypergraph H with N vertices and average degree d has independence number at least \(\frac{N} {{d^{1/2} }}\omega (d)\). We answer this question by constructing a 3-uniform, K 4 (3) -free hypergraph with independence number at most \(2\frac{N}{{{d^{1/2}}}}\). We also provide counterexamples to several related conjectures and improve the lower bound of some hypergraph Ramsey numbers.

Mathematics Subject Classification (2000)

05C65 05D05 05D10 


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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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