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

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

## Standard

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

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

## Harvard

*Discrete Mathematics*, vol. 340, no. 6, pp. 1172-1179. https://doi.org/10.1016/j.disc.2016.12.015

## APA

*Discrete Mathematics*,

*340*(6), 1172-1179. https://doi.org/10.1016/j.disc.2016.12.015

## Vancouver

## Author

## Bibtex

}

## 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 -