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An exact Turán result for the generalized triangle
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Pikhurko, Oleg (2008) An exact Turán result for the generalized triangle. Combinatorica, Vol.28 (No.2). pp. 187-208. doi:10.1007/s00493-008-2187-2 ISSN 0209-9683.
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Official URL: http://dx.doi.org/10.1007/s00493-008-2187-2
Abstract
Let Σ k consist of all k-graphs with three edges D 1, D 2, D 3 such that |D 1 ∩ D 2| = k − 1 and D 1 Δ D 2 ⊆ D 3. The exact value of the Turán function ex(n, Σ k ) was computed for k = 3 by Bollobás [Discrete Math. 8 (1974), 21-24] and for k = 4 by Sidorenko [Math Notes 41 (1987), 247-259].
Let the k-graph T k ∈ Σ k have edges Frankl and Füredi [J. Combin. Theory Ser. (A) 52 (1989), 129-147] conjectured that there is n 0 = n 0(k) such that ex(n, T k ) = ex(n, Σ k ) for all n ≥ n 0 and had previously proved this for k = 3 in [Combinatorica 3 (1983), 341-349]. Here we settle the case k = 4 of the conjecture.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Combinatorica | ||||
Publisher: | Springer | ||||
ISSN: | 0209-9683 | ||||
Official Date: | March 2008 | ||||
Dates: |
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Volume: | Vol.28 | ||||
Number: | No.2 | ||||
Page Range: | pp. 187-208 | ||||
DOI: | 10.1007/s00493-008-2187-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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