Pósa-type results for Berge hypergraphs

Nika Salia

doi:10.37236/11704

Pósa-type results for Berge hypergraphs

Nika Salia^*

^*Corresponding author for this work

Department of Mathematics

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

1 Scopus citations

Abstract

A Berge cycle of length k in a hypergraph H is a sequence of distinct vertices and hyperedges v₁, h₁, v₂, h₂, …, v_k, h_k such that v_i, v_i+1 ∈ h_i for all i ∈ [k], indices taken modulo k. Füredi, Kostochka, and Luo recently gave sharp Dirac-type minimum degree conditions that force non-uniform hypergraphs to have Hamiltonian Berge cycles. We give a sharp Pósa-type lower bound for r-uniform and non-uniform hypergraphs that force Hamiltonian Berge cycles.

Original language	English
Article number	P2.42
Journal	Electronic Journal of Combinatorics
Volume	31
Issue number	2
DOIs	https://doi.org/10.37236/11704
State	Published - 2024

Bibliographical note

Publisher Copyright:
© The author.

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.37236/11704

Cite this

@article{344ff78aa868410fb102853f10d3937a,

title = "P{\'o}sa-type results for Berge hypergraphs",

abstract = "A Berge cycle of length k in a hypergraph H is a sequence of distinct vertices and hyperedges v1, h1, v2, h2, …, vk, hk such that vi, vi+1 ∈ hi for all i ∈ [k], indices taken modulo k. F{\"u}redi, Kostochka, and Luo recently gave sharp Dirac-type minimum degree conditions that force non-uniform hypergraphs to have Hamiltonian Berge cycles. We give a sharp P{\'o}sa-type lower bound for r-uniform and non-uniform hypergraphs that force Hamiltonian Berge cycles.",

author = "Nika Salia",

note = "Publisher Copyright: {\textcopyright} The author.",

year = "2024",

doi = "10.37236/11704",

language = "English",

volume = "31",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Australian National University",

number = "2",

}

TY - JOUR

T1 - Pósa-type results for Berge hypergraphs

AU - Salia, Nika

PY - 2024

Y1 - 2024

N2 - A Berge cycle of length k in a hypergraph H is a sequence of distinct vertices and hyperedges v1, h1, v2, h2, …, vk, hk such that vi, vi+1 ∈ hi for all i ∈ [k], indices taken modulo k. Füredi, Kostochka, and Luo recently gave sharp Dirac-type minimum degree conditions that force non-uniform hypergraphs to have Hamiltonian Berge cycles. We give a sharp Pósa-type lower bound for r-uniform and non-uniform hypergraphs that force Hamiltonian Berge cycles.

AB - A Berge cycle of length k in a hypergraph H is a sequence of distinct vertices and hyperedges v1, h1, v2, h2, …, vk, hk such that vi, vi+1 ∈ hi for all i ∈ [k], indices taken modulo k. Füredi, Kostochka, and Luo recently gave sharp Dirac-type minimum degree conditions that force non-uniform hypergraphs to have Hamiltonian Berge cycles. We give a sharp Pósa-type lower bound for r-uniform and non-uniform hypergraphs that force Hamiltonian Berge cycles.

UR - https://www.scopus.com/pages/publications/85195135189

U2 - 10.37236/11704

DO - 10.37236/11704

M3 - Article

AN - SCOPUS:85195135189

SN - 1077-8926

VL - 31

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 2

M1 - P2.42

ER -

Pósa-type results for Berge hypergraphs

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this