In graph theory, a circle graph is the intersection graph of a set of chords of a circle. That is, it is an undirected graph whose vertices can be associated with chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
In graph theory, a circle graph is the intersection graph of a set of chords of a circle. That is, it is an undirected graph whose vertices can be associated with chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
The chords forming the 220-vertex 5-chromatic triangle-free circle graph of Ageev (1996), drawn as an arrangement of lines in the hyperbolic plane. The chromatic number of a circle graph is the minimum number of colors that can be used to color its chords so that no two crossing chords have the same color.