Editing Circle graph (section)

==Related graph classes==
[[File:Overlapgraph.svg|thumb|An interval system with five intervals and the corresponding overlap graph.]]
A graph is a circle graph if and only if it is the [[overlap graph]] of a set of intervals on a line. This is a graph in which the vertices correspond to the intervals, and two vertices are connected by an edge if the two intervals overlap, with neither containing the other.

The [[intersection graph]] of a set of intervals on a line is called the [[interval graph]].

[[String graph]]s, the [[intersection graph]]s of curves in the plane, include circle graphs as a special case.

Every [[distance-hereditary graph]] is a circle graph, as is every [[permutation graph]] and every [[indifference graph]]. Every [[outerplanar graph]] is also a circle graph.<ref>{{harvtxt|Wessel|Pöschel|1985}}; {{harvtxt|Unger|1988}}.</ref>

The circle graphs are generalized by the [[polygon-circle graph]]s, intersection graphs of polygons all inscribed in the same circle.<ref>{{citation
 | title = Circle graph
 | work = Information System on Graph Classes and their Inclusions 
 | url = http://www.graphclasses.org/classes/gc_132.html}}</ref>