Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sufficient spectral conditions for graphs being $k$-edge-Hamiltonian or
  $k$-Hamiltonian   A graph $G$ is $k$-edge-Hamiltonian if any collection of vertex-disjoint
paths with at most $k$ edges altogether belong to a Hamiltonian cycle in $G$. A
graph $G$ is $k$-Hamiltonian if for all $S\subseteq V(G)$ with $|S|\le k$, the
subgraph induced by $V(G)\setminus S$ has a Hamiltonian cycle. These two
concepts are classical extensions for the usual Hamiltonian graphs. In this
paper, we present some spectral sufficient conditions for a graph to be
$k$-edge-Hamiltonian and $k$-Hamiltonian in terms of the adjacency spectral
radius as well as the signless Laplacian spectral radius. Our results extend
the recent works proved by Li and Ning [Linear Multilinear Algebra 64 (2016)],
Nikiforov [Czechoslovak Math. J. 66 (2016)] and Li, Liu and Peng [Linear
Multilinear Algebra 66 (2018)]. Moreover, we shall prove a stability result for
graphs being $k$-Hamiltonian, which can be viewed as a complement of two recent
results of F\"{u}redi, Kostochka and Luo [Discrete Math. 340 (2017)] and
[Discrete Math. 342 (2019)].

5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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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: hep-lat
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The categories of this paper are: atom-ph