Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: NP-hardness results for partitioning graphs into disjoint cliques and a
  triangle-free subgraph   This paper investigates the computational complexity of deciding whether the
vertices of a graph can be partitioned into a disjoint union of cliques and a
triangle-free subgraph. This problem is known to be $\NP$-complete on arbitrary
graphs. We show that this problem remains $\NP$-complete even when restricted
to planar graphs and perfect graphs.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph