The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph
Research output: Contribution to journal › Article › peer-review
Authors
Colleges, School and Institutes
External organisations
- Graz Tech Univ
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.
Details
Original language | English |
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Pages (from-to) | 1172-1179 |
Number of pages | 8 |
Journal | Discrete Mathematics |
Volume | 340 |
Issue number | 6 |
Early online date | 20 Mar 2017 |
Publication status | Published - Jun 2017 |
Keywords
- Hamilton cycle, Hypergraph, Vertex degree