On hypergraphs without loose cycles

Jie Han; Yoshiharu Kohayakawa

doi:10.1016/j.disc.2017.12.015

On hypergraphs without loose cycles

Jie Han^*, Yoshiharu Kohayakawa

^*Corresponding author for this work

Universidade de São Paulo

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Recently, Mubayi and Wang showed that for r≥4 and ℓ≥3, the number of n-vertex r-graphs that do not contain any loose cycle of length ℓ is at most 2^{O(n^r−1(logn)^{(r−3)∕(r−2)})}. We improve this bound to 2^{O(n^r−1loglogn)}.

Original language	English
Pages (from-to)	946-949
Number of pages	4
Journal	Discrete Mathematics
Volume	341
Issue number	4
DOIs	https://doi.org/10.1016/j.disc.2017.12.015
Publication status	Published - Apr 2018
Externally published	Yes

Keywords

Hypergraph
Loose cycles

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10.1016/j.disc.2017.12.015

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Han, J., & Kohayakawa, Y. (2018). On hypergraphs without loose cycles. Discrete Mathematics, 341(4), 946-949. https://doi.org/10.1016/j.disc.2017.12.015

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title = "On hypergraphs without loose cycles",

abstract = "Recently, Mubayi and Wang showed that for r≥4 and ℓ≥3, the number of n-vertex r-graphs that do not contain any loose cycle of length ℓ is at most 2O(nr−1(logn)(r−3)∕(r−2)). We improve this bound to 2O(nr−1loglogn).",

keywords = "Hypergraph, Loose cycles",

author = "Jie Han and Yoshiharu Kohayakawa",

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AU - Han, Jie

AU - Kohayakawa, Yoshiharu

PY - 2018/4

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N2 - Recently, Mubayi and Wang showed that for r≥4 and ℓ≥3, the number of n-vertex r-graphs that do not contain any loose cycle of length ℓ is at most 2O(nr−1(logn)(r−3)∕(r−2)). We improve this bound to 2O(nr−1loglogn).

AB - Recently, Mubayi and Wang showed that for r≥4 and ℓ≥3, the number of n-vertex r-graphs that do not contain any loose cycle of length ℓ is at most 2O(nr−1(logn)(r−3)∕(r−2)). We improve this bound to 2O(nr−1loglogn).

KW - Hypergraph

KW - Loose cycles

UR - http://www.scopus.com/inward/record.url?scp=85041644452&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2017.12.015

DO - 10.1016/j.disc.2017.12.015

M3 - Article

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SN - 0012-365X

VL - 341

SP - 946

EP - 949

JO - Discrete Mathematics

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On hypergraphs without loose cycles

Abstract

Keywords

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