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• W3198642261 abstract "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 $mle n/7$. The bound on the number of edges is asymptotically best possible. This can be viewed as a generalization of the Erdős Matching Conjecture.We then use this result together with the absorbing method to determine the asymptotically best possible minimum $(k-3)$-degree threshold for $ell$-Hamiltonicity in $k$-graphs, where $kge 7$ 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 $ k,ell,d $." @default.
• W3198642261 created "2021-09-13" @default.
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• W3198642261 date "2021-08-28" @default.
• W3198642261 modified "2023-09-27" @default.
• W3198642261 title "Large $ Y_{k,b} $-tilings and Hamilton $ ell $-cycles in $k$-uniform hypergraphs" @default.
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