Abstract
AbstractWe resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs $$ H_{1} $$
H
1
and $$H_2$$
H
2
for all but six pairs $$(H_1,H_2)$$
(
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 $$(H_1,H_2)$$
(
H
1
,
H
2
)
-free graphs to five.
Funder
London Mathematical Society
Agence Nationale de la Recherche
Engineering and Physical Sciences Research Council
Leverhulme Trust
Masarykova Univerzita
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,General Computer Science
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