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- W3214488772 abstract "Given $kge3$ and $1leq ell< k$, an $(ell,k)$-cycle is one in which consecutive edges, each of size $k$, overlap in exactly $ell$ vertices. We study the smallest number of edges in $k$-uniform $n$-vertex hypergraphs which do not contain hamiltonian $(ell,k)$-cycles, but once a new edge is added, such a cycle is promptly created. It has been conjectured that this number is of order $n^ell$ and confirmed for $ellin{1,k/2,k-1}$, as well as for the upper range $0.8kleq ellleq k-1$. Here we extend the validity of this conjecture to the lower-middle range $(k-1)/3leell<k/2$." @default.
- W3214488772 created "2021-11-22" @default.
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- W3214488772 date "2021-11-09" @default.
- W3214488772 modified "2023-10-01" @default.
- W3214488772 title "Constructing sparsest $ell$-hamiltonian saturated $k$-uniform hypergraphs for a wide range of $ell$" @default.
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