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Circle Graphs Can Be Recognized in Linear Time

Authors Christophe Paul , Ignaz Rutter

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LIPIcs.STACS.2026.72.pdf
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  • 20 pages

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Graph theory
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Graph algorithms analysis
Keywords
  • graph classes
  • circle graphs
  • graph algorithms

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Abstract

To date, the best circle graph recognition algorithm, due to Gioan et al. [E. Gioan et al., 2014] runs in almost linear time as it relies on a split decomposition algorithm [E. Gioan et al., 2014] that uses the union-find data-structure [B.A. Galler and M.J. Fischer, 1964; R. Tarjan, 1975]. We show that in the case of circle graphs, the PC-tree data-structure [W. K. Shih and W. L. Hsu, 1999] 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.

Cite As Get BibTex

Christophe Paul and Ignaz Rutter. Circle Graphs Can Be Recognized in Linear Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 72:1-72:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.72

Author Details

Christophe Paul
  • CNRS, Université Montpellier, France
Ignaz Rutter
  • University of Passau, Germany

Funding

  • Paul, Christophe: Research supported by ANR-DFG project GODASse ANR-24-CE48-4377.

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