Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Relative Length of Long Paths and Cycles in Graphs   Let $G$ be a graph on $n$ vertices, $p$ the order of a longest path and
$\kappa$ the connectivity of $G$. In 1989, Bauer, Broersma Li and Veldman
proved that if $G$ is a 2-connected graph with $d(x)+d(y)+d(z)\ge n+\kappa$ for
all triples $x,y,z$ of independent vertices, then $G$ is hamiltonian. In this
paper we improve this result by reducing the lower bound $n+\kappa$ to
$p+\kappa$.

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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph