Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: List-three-coloring graphs with no induced $P_6+rP_3$   For an integer $r$, the graph $P_6+rP_3$ has $r+1$ components, one of which
is a path on $6$ vertices, and each of the others is a path on $3$ vertices. In
this paper we provide a polynomial-time algorithm to test if a graph with no
induced subgraph isomorphic to $P_6+rP_3$ is three-colorable. We also solve the
list version of this problem, where each vertex is assigned a list of possible
colors, which is a subset of $\{1,2,3\}$.

5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ