The complexity of the vertexminor problem
Abstract
A graph H is a vertexminor of a graph G if it can be reached from G by the successive application of local complementations and vertex deletions. Vertexminors have been the subject of intense study in graph theory over the last decades and have found applications in other fields such as quantum information theory. Therefore it is natural to consider the computational complexity of deciding whether a given graph G has a vertexminor isomorphic to another graph H, which was previously unknown. Here we prove that this decision problem is NPcomplete, even when restricting H, G to be circle graphs, a class of graphs that has a natural relation to vertexminors.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.05689
 Bibcode:
 2019arXiv190605689D
 Keywords:

 Mathematics  Combinatorics;
 Quantum Physics
 EPrint:
 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1805.05306