Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decompositions of complete uniform hypergraphs into Hamilton Berge
  cycles   In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if $n$ divides
$\binom{n}{k}$, then the complete $k$-uniform hypergraph on $n$ vertices has a
decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an
alternating sequence $v_1,e_1,v_2,\dots,v_n,e_n$ of distinct vertices $v_i$ and
distinct edges $e_i$ so that each $e_i$ contains $v_i$ and $v_{i+1}$. So the
divisibility condition is clearly necessary. In this note, we prove that the
conjecture holds whenever $k \ge 4$ and $n \ge 30$. Our argument is based on
the Kruskal-Katona theorem. The case when $k=3$ was already solved by Verrall,
building on results of Bermond.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: physics