Affiliation:
1. University of Bremen, Bremen, Germany
Abstract
We give an isomorphism test that runs in time
n
polylog(
h
)
on all
n
-vertex graphs excluding some
h
-vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time
n
polylog(
h
)
(Babai, STOC 2016) and
n
{f(h)
for some function
f
(Grohe and Marx, SIAM J. Comp., 2015).
Our result also unifies and extends previous isomorphism tests for graphs of maximum degree
d
running in time
n
polylog(
d
)
(SIAM J. Comp., 2023) and for graphs of Hadwiger number
h
running in time
n
polylog(
h
)
(SIAM J. Comp., 2023).
Funder
European Research Council
Publisher
Association for Computing Machinery (ACM)