Abstract
We show that for sufficiently large n, every 3-uniform hypergraph on n vertices with minimum vertex degree at least (n-12)-(34n-2)+c, where c=. 2 if n∈4N and c=. 1 if n∈2N-4N, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of Buß, Hàn and Schacht who proved the corresponding asymptotical result.
Original language | English |
---|---|
Pages (from-to) | 70-96 |
Number of pages | 27 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 114 |
DOIs | |
Publication status | Published - 1 Sept 2015 |
Externally published | Yes |
Keywords
- Absorbing method
- Hamilton cycle
- Hypergraph
- Regularity lemma