Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On perfect packings in dense graphs   We say that a graph G has a perfect H-packing if there exists a set of
vertex-disjoint copies of H which cover all the vertices in G. We consider
various problems concerning perfect H-packings: Given positive integers n, r,
D, we characterise the edge density threshold that ensures a perfect
K_r-packing in any graph G on n vertices and with minimum degree at least D. We
also give two conjectures concerning degree sequence conditions which force a
graph to contain a perfect H-packing. Other related embedding problems are also
considered. Indeed, we give a structural result concerning K_r-free graphs that
satisfy a certain degree sequence condition.

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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex