A circle graph is an undirected graph that represents the intersection graph of a set of chords of a circle.
for every circle graph G we can draw a circle and a set of chords of that circle such that the chords are in one-to-one correspondence with the vertices of G and two chords cross each other if and only if the corresponding vertices are adjacent in G. An example of a circle graph and a corresponding chord drawing is given in Figure 3.