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.

This diagram with labels depicts and explains the details of

*Circle Graph. *## Circle Graph