Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shadow of Hypergraphs with Bounded Degree   We study the size of the shadow of $k$-uniform hypergraphs with bounded
degree. Lower bounds on the ratio of the size of the shadow and the size of the
hypergraph are given as a function of the degree bound and $k$. We show that
cliques are extremal for a long range of degree bounds, but not for every
bound. We give a general, but not sharp lower bound on the shadow ratio and
show, that sometimes we can get extremal hypergraphs by deleting disjoint
maximal matchings from a clique.

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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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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: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an