Circle graphs can be recognized in linear time
Data Structures and Algorithms
2026-01-01 v2 Discrete Mathematics
Abstract
To date, the best circle graph recognition algorithm runs in almost linear time as it relies on a split decomposition algorithm that uses the union-find data-structure. We show that in the case of circle graphs, the PC-tree data-structure allows one to avoid the union-find data-structure to compute the split decomposition in linear time. As a consequence, we obtain the first linear-time recognition algorithm for circle graphs.
Keywords
Cite
@article{arxiv.2512.23492,
title = {Circle graphs can be recognized in linear time},
author = {Christophe Paul and Ignaz Rutter},
journal= {arXiv preprint arXiv:2512.23492},
year = {2026}
}
Comments
To appear in 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)