English

Practical and Efficient Circle Graph Recognition

Data Structures and Algorithms 2012-11-01 v3 Discrete Mathematics

Abstract

Circle graphs are the intersection graphs of chords in a circle. This paper presents the first sub-quadratic recognition algorithm for the class of circle graphs. Our algorithm is O(n + m) times the inverse Ackermann function, {\alpha}(n + m), whose value is smaller than 4 for any practical graph. The algorithm is based on a new incremental Lexicographic Breadth-First Search characterization of circle graphs, and a new efficient data-structure for circle graphs, both developed in the paper. The algorithm is an extension of a Split Decomposition algorithm with the same running time developed by the authors in a companion paper.

Keywords

Cite

@article{arxiv.1104.3284,
  title  = {Practical and Efficient Circle Graph Recognition},
  author = {Emeric Gioan and Christophe Paul and Marc Tedder and Derek Corneil},
  journal= {arXiv preprint arXiv:1104.3284},
  year   = {2012}
}
R2 v1 2026-06-21T17:55:09.005Z