# Category: Intersection classes of graphs

Interval graph
In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line,with a vertex for each interval and an edge between vertices whose intervals intersect. It is
Ptolemaic graph
In graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek astronomer and mathematician Ptolemy. The Pto
Polygon-circle graph
In the mathematical discipline of graph theory, a polygon-circle graph is an intersection graph of a set of convex polygons all of whose vertices lie on a common circle. These graphs have also been ca
Intersection number (graph theory)
In the mathematical field of graph theory, the intersection number of a graph is the smallest number of elements in a representation of as an intersection graph of finite sets. In such a representatio
String graph
In graph theory, a string graph is an intersection graph of curves in the plane; each curve is called a "string". Given a graph G, G is a string graph if and only if there exists a set of curves, or s
Circular-arc graph
In graph theory, a circular-arc graph is the intersection graph of a set of arcs on the circle. It has one vertex for each arc in the set, and an edge between every pair of vertices corresponding to a
Indifference graph
In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers a
Intersection graph
In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an intersection graph, but some important special cl
Block graph
In graph theory, a branch of combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component (block) is a clique. Block graphs are sometimes
Chordal graph
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of
Line graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following w
Distance-hereditary graph
In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances in any connected induced subgraph are the sa
Circle graph
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that t
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can
Trapezoid graph
In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that contain interval graphs and permutation graphs as
Unit disk graph
In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in the family, and with an
Permutation graph
In the mathematical field of graph theory, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs of elements that are reversed by the p
Split graph
In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Földes and Hammer ,