Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Graphs for which the Maximum Multiplicity of an Eigenvalue is Two   Characterized are all simple undirected graphs $G$ such that any real
symmetric matrix that has graph $G$ has no eigenvalues of multiplicity more
than 2. All such graphs are partial 2-trees (and this follows from a result for
rather general fields), but only certain partial 2-trees guarantee maximum
multiplicity 2. Among partial linear 2-trees, they are only those whose
vertices can be covered by two "parallel" induced paths. The remaining graphs
that guarantee maximum multiplicity 2 are comprised by certain identified
families of "exceptional" partial 2-trees that are not linear.

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The categories of this paper are: stat
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph