Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: NP-Completeness of Hamiltonian Cycle Problem on Rooted Directed Path
  Graphs   The Hamiltonian cycle problem is to decide whether a given graph has a
Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing
Letters, 23, 195-200) proved that the Hamiltonian Cycle Problem is NP-Complete
even for undirected path graphs and left the Hamiltonian cycle problem open for
directed path graphs. Narasimhan (1989, Information Processing Letters, 32,
167-170) proved that the Hamiltonian Cycle Problem is NP-Complete even for
directed path graphs and left the Hamiltonian cycle problem open for rooted
directed path graphs. In this paper we resolve this open problem by proving
that the Hamiltonian Cycle Problem is also NP-Complete for rooted directed path
graphs.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math