Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near Perfect Matchings in $k$-uniform Hypergraphs II   Suppose $k\nmid n$ and $H$ is an $n$-vertex $k$-uniform hypergraph. A near
perfect matching in $H$ is a matching of size $\lfloor n/k\rfloor$. We give a
divisibility barrier construction that prevents the existence of near perfect
matchings in $H$. This generalizes the divisibility barrier for perfect
matchings. We give a conjecture on the minimum $d$-degree threshold forcing a
(near) perfect matching in $H$ which generalizes a well-known conjecture on
perfect matchings. We also verify our conjecture in various cases. Our proof
makes use of the lattice-based absorbing method that the author used recently
to solve two other problems on matching and tilings for hypergraphs.

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The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc