Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The k-path vertex cover: general bounds and chordal graphs   For an integer $k\ge 3$, a $k$-path vertex cover of a graph $G=(V,E)$ is a
set $T\subseteq V$ that shares a vertex with every path subgraph of order $k$
in $G$. The minimum cardinality of a $k$-path vertex cover is denoted by
$\psi_k(G)$. We give estimates -- mostly upper bounds -- on $\psi_k(G)$ in
terms of various parameters, including vertex degrees and the number of
vertices and edges. The problem is also considered on chordal graphs and planar
graphs.

10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph