Paper Info
Title
An exact Turán result for the generalized triangle
Abstract
Let Σ k consist of all k-graphs with three edges D 1, D 2, D 3 such that |D 1 驴 D 2| = k 驴 1 and D 1 Δ D 2 驴 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 驴 Σ k have edges $$ \{ 1, \ldots ,k\} , \{ 1,2, \ldots ,k - 1,k + 1\} , and \{ k,k + 1, \ldots ,2k - 1\} . $$ 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 驴 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.
Year
DOI
Venue
2008
10.1007/s00493-008-2187-2
Combinatorica
Keywords
Field
DocType
theory ser,edges d,discrete math,case k,exact tur,j. combin,n function,n result,exact value,math notes,generalized triangle
Discrete mathematics,Combinatorics,Conjecture,Mathematics
Journal
Volume
Issue
ISSN
28
2
0209-9683
Citations 
PageRank 
References 
16
1.05
14
Authors
1
Name
Order
Citations
PageRank
Oleg Pikhurko131847.03