Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Query Complexity of Subgraph Containment with Constant-sized
  Certificates   We study the quantum query complexity of constant-sized subgraph containment.
Such problems include determining whether an $ n $-vertex graph contains a
triangle, clique or star of some size. For a general subgraph $ H $ with $ k $
vertices, we show that $ H $ containment can be solved with quantum query
complexity $ O(n^{2-\frac{2}{k}-g(H)}) $, with $ g(H) $ a strictly positive
function of $ H $. This is better than $ \tilde{O}\s{n^{2-2/k}} $ by Magniez et
al. These results are obtained in the learning graph model of Belovs.

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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex