Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Maximum Order of Induced Paths and Induced Forests in Regular
  Graphs   Let $G$ be a graph and $a(G)$, LIF$(G)$ denote the maximum orders of an
induced forest and an induced linear forest of $G$, respectively. It is
well-known that if $G$ is an $r$-regular graph of order $n$, then $a(G) \geq
\frac{2}{r+1}n$. In this paper, we generalize this result by showing that
LIF$(G) \geq \frac{2}{r+1}n$. It was proved that for every graph $G$, $a(G)
\geq \sum_{i=1}^{n}\frac{2}{d_i+1}$, where $d_1, \ldots, d_n$ is the degree
sequence of $G$. Here, we conjecture that for every graph $G$ with $\delta(G)
\geq 2$, LIF$(G) \geq \sum_{i=1}^{n}\frac{2}{d_i+1}$.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ