The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph

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The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph. / Cooley, Oliver; Mycroft, Richard.

In: Discrete Mathematics, Vol. 340, No. 6, 06.2017, p. 1172-1179.

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@article{3c132393f00347c583cab37bcc162f6f,
title = "The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph",
abstract = "We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{5}{9} + o(1) \right)\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, B\{"}ottcher, Cooley and Mycroft. ",
keywords = "Hamilton cycle, Hypergraph, Vertex degree",
author = "Oliver Cooley and Richard Mycroft",
year = "2017",
month = jun,
doi = "10.1016/j.disc.2016.12.015",
language = "English",
volume = "340",
pages = "1172--1179",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "6",

}

RIS

TY - JOUR

T1 - The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph

AU - Cooley, Oliver

AU - Mycroft, Richard

PY - 2017/6

Y1 - 2017/6

N2 - We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{5}{9} + o(1) \right)\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, B\"ottcher, Cooley and Mycroft.

AB - We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{5}{9} + o(1) \right)\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, B\"ottcher, Cooley and Mycroft.

KW - Hamilton cycle

KW - Hypergraph

KW - Vertex degree

U2 - 10.1016/j.disc.2016.12.015

DO - 10.1016/j.disc.2016.12.015

M3 - Article

VL - 340

SP - 1172

EP - 1179

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 6

ER -