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Circle graphs can be recognized in linear time

Published: December 29, 2025 | arXiv ID: 2512.23492v1

By: Christophe Paul, Ignaz Rutter

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.

Category
Computer Science:
Data Structures and Algorithms