Large $ Y_{k,b} $-tilings and Hamilton $ \ell $-cycles in $k$-uniform hypergraphs
| Autor: | Gan, Luyining, Han, Jie, Sun, Lin, Wang, Guanghui |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $Y_{3,2}$ be the $3$-uniform hypergraph with two edges intersecting in two vertices. Our main result is that any $n$-vertex 3-uniform hypergraph with at least $\binom{n}{3} - \binom{n-m+1}{3} + o(n^3)$ edges contains a collection of $m$ vertex-disjoint copies of $Y_{3,2}$, for $m\le n/7$. The bound on the number of edges is asymptotically best possible. This problem generalizes the Matching Conjecture of Erd\H{o}s. We then use this result combined with the absorbing method to determine the asymptotically best possible minimum $(k-3)$-degree threshold for $\ell$-Hamiltonicity in $k$-graphs, where $k\ge 7$ is odd and $\ell=(k-1)/2$. Moreover, we give related results on $ Y_{k,b} $-tilings and Hamilton $ \ell $-cycles with $ d $-degree for some other values of $ k,\ell,d $. Comment: arXiv admin note: text overlap with arXiv:0903.2867 by other authors |
| Databáze: | arXiv |
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