The codegree Turán density of tight cycles minus one edge

Simón Piga; Marcelo Sales; Bjarne Schülke

doi:10.1017/S0963548323000196

The codegree Turán density of tight cycles minus one edge

Simón Piga^*, Marcelo Sales, Bjarne Schülke

^*Corresponding author for this work

Mathematics

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Abstract

Given α>0 and an integer ℓ≥5, we prove that every sufficiently large 3 -uniform hypergraph H on n vertices in which every two vertices are contained in at least αn
edges contains a copy of C−ℓ , a tight cycle on ℓ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidický.

Original language	English
Pages (from-to)	1-4
Journal	Combinatorics, Probability and Computing
Early online date	5 Jul 2023
DOIs	https://doi.org/10.1017/S0963548323000196
Publication status	E-pub ahead of print - 5 Jul 2023

Keywords

codegree density
hypergraphs

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10.1017/S0963548323000196Licence: Creative Commons: Attribution (CC BY)

PigaS2023TheCodegreeFinal published version, 315 KBLicence: Creative Commons: Attribution (CC BY)

Cite this

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title = "The codegree Tur{\'a}n density of tight cycles minus one edge",

abstract = "Given α>0 and an integer ℓ≥5, we prove that every sufficiently large 3 -uniform hypergraph H on n vertices in which every two vertices are contained in at least αn edges contains a copy of C−ℓ , a tight cycle on ℓ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidick{\'y}.",

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author = "Sim{\'o}n Piga and Marcelo Sales and Bjarne Sch{\"u}lke",

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AU - Piga, Simón

AU - Sales, Marcelo

AU - Schülke, Bjarne

PY - 2023/7/5

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N2 - Given α>0 and an integer ℓ≥5, we prove that every sufficiently large 3 -uniform hypergraph H on n vertices in which every two vertices are contained in at least αn edges contains a copy of C−ℓ , a tight cycle on ℓ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidický.

AB - Given α>0 and an integer ℓ≥5, we prove that every sufficiently large 3 -uniform hypergraph H on n vertices in which every two vertices are contained in at least αn edges contains a copy of C−ℓ , a tight cycle on ℓ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidický.

KW - codegree density

KW - hypergraphs

U2 - 10.1017/S0963548323000196

DO - 10.1017/S0963548323000196

M3 - Article

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SP - 1

EP - 4

JO - Combinatorics, Probability and Computing

JF - Combinatorics, Probability and Computing

ER -

The codegree Turán density of tight cycles minus one edge

Abstract

Keywords

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