Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral radius and traceability of connected claw-free graphs   Let $G$ be a connected claw-free graph on $n$ vertices and $\overline{G}$ be
its complement graph. Let $\mu(G)$ be the spectral radius of $G$. Denote by
$N_{n-3,3}$ the graph consisting of $K_{n-3}$ and three disjoint pendent edges.
In this note we prove that: (1) If $\mu(G)\geq n-4$, then $G$ is traceable
unless $G=N_{n-3,3}$. (2) If $\mu(\overline{G})\leq \mu(\overline{N_{n-3,3}})$
and $n\geq 24$, then $G$ is traceable unless $G=N_{n-3,3}$. Our works are
counterparts on claw-free graphs of previous theorems due to Lu et al., and
Fiedler and Nikiforov, respectively.

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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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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: chem-ph
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The categories of this paper are: plasm-ph