A note on the Turán number of a Berge odd cycle

Gerbner, Dániel

doi:10.48550/arxiv.1903.01002

Cited by 2 publications

(2 citation statements)

References 17 publications

(49 reference statements)

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“…Füredi and Özkahya [21] obtained better constant factors (depending on k). Further improvements were obtained for even k by Gerbner, Methuku and Vizer [24], also by Gerbner, Methuku and Palmer [23], and for odd k by Gerbner [22]. For s ≥ 4, Győri and Lemons [26] showed that ex(n, s,…”

Section: Preliminariesmentioning

confidence: 96%

Anti-Ramsey Numbers of Paths and Cycles in Hypergraphs

Gu¹,

Li²,

Shi³

2020

SIAM J. Discrete Math.

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The anti-Ramsey problem was introduced by Erdős, Simonovits and Sós in 1970s. The anti-Ramsey number of a hypergraph H, ar(n, s, H), is the smallest integer c such that in any coloring of the edges of the s-uniform complete hypergraph on n vertices with exactly c colors, there is a copy of H whose edges have distinct colors. In this paper, we determine the anti-Ramsey numbers of linear paths and loose paths in hypergraphs for sufficiently large n, and give bounds for the anti-Ramsey numbers of Berge paths. Similar exact anti-Ramsey numbers are obtained for linear/loose cycles, and bounds are obtained for Berge cycles. Our main tools are path extension technique and stability results on hypergraph Turán problems of paths and cycles.

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Section: Preliminariesmentioning

confidence: 96%

Anti-Ramsey Numbers of Paths and Cycles in Hypergraphs

Gu¹,

Li²,

Shi³

2020

SIAM J. Discrete Math.

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“…Our proof is based on the proof of Lemma 6. We use the following lemma from [11] (most of which already appears in [13]).…”

Section: Generalized Hypergraph Turán Problemsmentioning

confidence: 99%

Hypergraph based Berge hypergraphs

Balko¹,

Gerbner²,

Kang³

et al. 2019

Preprint

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Fix a hypergraph F. A hypergraph H is called a Berge copy of F or Berge-F if we can choose a subset of each hyperedge of H to obtain a copy of F. A hypergraph H is Berge-F-free if it does not contain a subhypergraph which is Berge copy of F. This is a generalization of the usual, graph based Berge hypergraphs, where F is a graph.In this paper, we study extremal properties of hypergraph based Berge hypergraphs and generalize several results from the graph based setting. In particular, we show

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A note on the Turán number of a Berge odd cycle

Abstract: In this note we obtain upper bounds on the number of hyperedges in 3-uniform hypergraphs not containing a Berge cycle of given odd length. We improve the bound given by Füredi and Özkahya. The result follows from a more general theorem. We also obtain some new results for Berge cliques.

Cited by 2 publications

References 17 publications

Anti-Ramsey Numbers of Paths and Cycles in Hypergraphs

Anti-Ramsey Numbers of Paths and Cycles in Hypergraphs

Hypergraph based Berge hypergraphs

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