Circle graphs can be recognized in linear time

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.

To appear in 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)