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تسجيل مستخدم جديدLarge $ Y_{k,b} $-tilings and Hamilton $ ell $-cycles in $k$-uniform hypergraphs
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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 ErdH{o}s 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 $.
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We show that, for a natural notion of quasirandomness in $k$-uniform hypergraphs, any quasirandom $k$-uniform hypergraph on $n$ vertices with constant edge density and minimum vertex degree $Omega(n^{k-1})$ contains a loose Hamilton cycle. We also gi
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