Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Length of Long Paths and Cycles in Graphs   For a graph $G$, $n$ denotes the order of $G$, $p$ the order of a longest
path in $G$ and $c$ the order of a longest cycle. We show that if $G$ is a
2-connected graph such that $d(x)+d(y)+d(z)\ge p+2$ for all triples $x,y,z$ of
independent vertices, then $c\ge p-1$. This improves results of Nash-Williams
(in terms of minimum degree $\delta$ and order $n$), Bondy (in terms of degree
sum $\sigma_{3}$ and order $n$), and Enomoto, Heuvel, Kaneko and Saito (in
terms of degree sum $\sigma_3$, order $n$ and relative length $diff(G)=p-c$).

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph