Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph Isomorphism for $(H_1,H_2)$-free Graphs: An Almost Complete
  Dichotomy   We resolve the computational complexity of Graph Isomorphism for classes of
graphs characterized by two forbidden induced subgraphs $H_1$ and $H_2$ for all
but six pairs $(H_1,H_2)$. Schweitzer had previously shown that the number of
open cases was finite, but without specifying the open cases. Grohe and
Schweitzer proved that Graph Isomorphism is polynomial-time solvable on graph
classes of bounded clique-width. Our work combines known results such as these
with new results. By exploiting a relationship between Graph Isomorphism and
clique-width, we simultaneously reduce the number of open cases for boundedness
of clique-width for $(H_1,H_2)$-free graphs to five.

17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys