Practical and Efficient Circle Graph Recognition

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, α(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.