Linear trees in uniform hypergraphs
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Publication:2509754
DOI10.1016/J.EJC.2013.06.022zbMATH Open1296.05140arXiv1204.1936OpenAlexW1964094911MaRDI QIDQ2509754
Publication date: 29 July 2014
Published in: European Journal of Combinatorics (Search for Journal in Brave)
Abstract: Given a tree T on v vertices and an integer k exceeding one. One can define the k-expansion T^k as a k-uniform linear hypergraph by enlarging each edge with a new, distinct set of (k-2) vertices. Then T^k has v+ (v-1)(k-2) vertices. The aim of this paper is to show that using the delta-system method one can easily determine asymptotically the size of the largest T^k-free n-vertex hypergraph, i.e., the Turan number of T^k.
Full work available at URL: https://arxiv.org/abs/1204.1936
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Related Items (16)
Turán numbers for hypergraph star forests ⋮ Turán problems and shadows. II: Trees ⋮ On vertex independence number of uniform hypergraphs ⋮ Turán numbers of Berge trees ⋮ Hypergraph Turán numbers of linear cycles ⋮ The structure of large intersecting families ⋮ Extremal Results for Berge Hypergraphs ⋮ $t$-Wise Berge and $t$-Heavy Hypergraphs ⋮ Non-trivial \(d\)-wise intersecting families ⋮ Lower bounds on Tuza constants for transversals in linear uniform hypergraphs ⋮ The junta method for hypergraphs and the Erdős-Chvátal simplex conjecture ⋮ Turán numbers for Berge-hypergraphs and related extremal problems ⋮ Decomposing uniform hypergraphs into uniform hypertrees and single edges ⋮ Turán numbers of general star forests in hypergraphs ⋮ Asymptotic Turán number for linear 5-cycle in 3-uniform linear hypergraphs ⋮ Turán Problems and Shadows III: Expansions of Graphs
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