Turán Numbers of Complete 3-Uniform Berge-Hypergraphs

Turán Numbers of Complete 3-Uniform Berge-Hypergraphs Graphs and Combinatorics https://doi.org/10.1007/s00373-018-1900-1 ORIGINAL PAPER Turán Numbers of Complete 3-Uniform Berge-Hypergraphs 1 2 L. Maherani · M. Shahsiah Received: 6 August 2017 / Revised: 15 March 2018 © Springer Japan KK, part of Springer Nature 2018 Abstract Given a family F of r-graphs, the Turán number of F for a given positive integer N, denoted by ex (N , F ), is the maximum number of edges of an r-graph on N vertices that does not contain any member of F as a subgraph. For given r ≥ 3, a (r ) complete r-uniform Berge-hypergraph, denoted by K ,isan r-uniform hypergraph of order n with the core sequence v ,v ,...,v as the vertices and distinct edges 1 2 n (r ) e , 1 ≤ i < j ≤ n, where every e contains both v and v .Let F be the ij ij i j family of complete r-uniform Berge-hypergraphs of order n. We determine precisely (3) (3) ex (N , F ) for N ≥ n ≥ 13. We also find the extremal hypergraphs avoiding F . n n Keywords Turán number · Extremal hypergraph · Berge-hypergraph Mathematics Subject Classification 05C65 · 05C35 · 05D05 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Graphs and Combinatorics Springer Journals

Turán Numbers of Complete 3-Uniform Berge-Hypergraphs

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Publisher
Springer Japan
Copyright
Copyright © 2018 by Springer Japan KK, part of Springer Nature
Subject
Mathematics; Combinatorics; Engineering Design
ISSN
0911-0119
eISSN
1435-5914
D.O.I.
10.1007/s00373-018-1900-1
Publisher site
See Article on Publisher Site

Abstract

Graphs and Combinatorics https://doi.org/10.1007/s00373-018-1900-1 ORIGINAL PAPER Turán Numbers of Complete 3-Uniform Berge-Hypergraphs 1 2 L. Maherani · M. Shahsiah Received: 6 August 2017 / Revised: 15 March 2018 © Springer Japan KK, part of Springer Nature 2018 Abstract Given a family F of r-graphs, the Turán number of F for a given positive integer N, denoted by ex (N , F ), is the maximum number of edges of an r-graph on N vertices that does not contain any member of F as a subgraph. For given r ≥ 3, a (r ) complete r-uniform Berge-hypergraph, denoted by K ,isan r-uniform hypergraph of order n with the core sequence v ,v ,...,v as the vertices and distinct edges 1 2 n (r ) e , 1 ≤ i < j ≤ n, where every e contains both v and v .Let F be the ij ij i j family of complete r-uniform Berge-hypergraphs of order n. We determine precisely (3) (3) ex (N , F ) for N ≥ n ≥ 13. We also find the extremal hypergraphs avoiding F . n n Keywords Turán number · Extremal hypergraph · Berge-hypergraph Mathematics Subject Classification 05C65 · 05C35 · 05D05

Journal

Graphs and CombinatoricsSpringer Journals

Published: May 28, 2018

References

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