Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Erdos-Gallai Stability Theorem for Linear Forests   The Erd\H{o}s-Gallai Theorem states that every graph of average degree more
than $l-2$ contains a path of order $l$ for $l\ge 2$. In this paper, we obtain
a stability version of the Erd\H{o}s-Gallai Theorem in terms of minimum degree.
Let $G$ be a connected graph of order $n$ and
$F=(\bigcup_{i=1}^kP_{2a_i})\bigcup(\bigcup_{i=1}^lP_{2b_i+1})$ be $k+l$
disjoint paths of order $2a_1, \ldots, 2a_{k}, 2b_1+1, \ldots, 2b_l+1,$
respectively, where $k\ge 0$, $0\le l\le 2$, and $k+l\geq 2$. If the minimum
degree $\delta(G)\ge \sum_{i=1}^ka_i+\sum_{i=1}^lb_i-1$, then $F\subseteq G$
except several classes of graphs for sufficiently large $n$, which extends and
strengths the results of Ali and Staton for an even path and Yuan and Nikiforov
for an odd path.

11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th