Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing sparsest $\ell$-hamiltonian saturated $k$-uniform
  hypergraphs for a wide range of $\ell$   Given $k\ge3$ and $1\leq \ell< k$, 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 $\ell\in\{1,k/2,k-1\}$, as well as for the
upper range $0.8k\leq \ell\leq k-1$. Here we extend the validity of this
conjecture to the lower-middle range $(k-1)/3\le\ell<k/2$.

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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph