Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonicity is Hard in Thin or Polygonal Grid Graphs, but Easy in Thin
  Polygonal Grid Graphs   In 2007, Arkin et al. initiated a systematic study of the complexity of the
Hamiltonian cycle problem on square, triangular, or hexagonal grid graphs,
restricted to polygonal, thin, superthin, degree-bounded, or solid grid graphs.
They solved many combinations of these problems, proving them either
polynomially solvable or NP-complete, but left three combinations open. In this
paper, we prove two of these unsolved combinations to be NP-complete:
Hamiltonicity of Square Polygonal Grid Graphs and Hamiltonicity of Hexagonal
Thin Grid Graphs. We also consider a new restriction, where the grid graph is
both thin and polygonal, and prove that Hamiltonicity then becomes polynomially
solvable for square, triangular, and hexagonal grid graphs.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org