Solving Turán's tetrahedron problem for the ℓ2$\ell _2$ ‐norm

  title={Solving Tur{\'a}n's tetrahedron problem for the ℓ2\$\ell \_2\$ ‐norm},
  author={J{\'o}zsef Balogh and Felix Christian Clemen and Bernard Lidick'y},
  journal={Journal of the London Mathematical Society},
Turán's famous tetrahedron problem is to compute the Turán density of the tetrahedron K43$K_4^3$ . This is equivalent to determining the maximum ℓ1$\ell _1$ ‐norm of the codegree vector of a K43$K_4^3$ ‐free n$n$ ‐vertex 3‐uniform hypergraph. We introduce a new way for measuring extremality of hypergraphs and determine asymptotically the extremal function of the tetrahedron in our notion. The codegree squared sum, co2(G)$\mbox{co}_2(G)$ , of a 3‐uniform hypergraph G$G$ is the sum of codegrees… 
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Hypergraph Turán problems, Surveys in combinatorics 2011, London Math

  • Soc. Lecture Note Ser., vol. 392, Cambridge Univ. Press, Cambridge,
  • 2011