Testing isomorphism of chordal graphs of bounded leafage is fixed-parameter tractable
Abstract
The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general graph isomorphism problem. Every chordal graph can be represented as the intersection graph of some subtrees of a representing tree, and the leafage of a chordal graph is defined to be the minimum number of leaves in a representing tree for it. We prove that chordal graph isomorphism is fixed parameter tractable with leafage as parameter. In the process we introduce the problem of isomorphism testing for higher-order hypergraphs and show that finding the automorphism group of order- hypergraphs with vertex color classes of size is fixed parameter tractable for any constant and as fixed parameter.
Cite
@article{arxiv.2107.10689,
title = {Testing isomorphism of chordal graphs of bounded leafage is fixed-parameter tractable},
author = {Vikraman Arvind and Roman Nedela and Ilia Ponomarenko and Peter Zeman},
journal= {arXiv preprint arXiv:2107.10689},
year = {2022}
}