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...

In the mathematical field of graph theory, the intersection number of a graph G = ( V , E ) {\displaystyle G=(V,E)} is the smallest number of elements...

line graphs (intersection graphs of the edges of a graph), and clique graphs (intersection graphs of the maximal cliques of a graph). Every graph is an...

intervals intersect. It is the intersection graph of the intervals. Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear...

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...

perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree. They are sometimes...

descriptions of redirect targets Intersection graph – Graph representing intersections between given sets Intersection theory – Branch of algebraic geometry...

In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a...

its intersection graph is called a coin graph; more generally, intersection graphs of interior-disjoint geometric objects are called tangency graphs or...

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...

In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain...

interval graph; the intersection graph of unit disks in the plane is a unit disk graph. The Circle packing theorem states that the intersection graphs of non-crossing...

In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are...

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...

In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar...

(1998) "Modern Graph Theory", Springer, ISBN 0-387-98488-7 p. 9 Kashiwabara, Toshinobu (1981), "Algorithms for some intersection graphs", in Saito, Nobuji;...

gives rise to the field of spectral graph theory. Dual to the observation above that every graph is an intersection graph is the fact that every partially...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer...

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...

cospectral graphs are the point-collinearity graphs and the line-intersection graphs of point-line geometries. These graphs are always cospectral but are often...

Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory...

Block graphs may be characterized as the intersection graphs of the blocks of arbitrary undirected graphs. Block graphs are exactly the graphs for which...

reversed by the permutation. Permutation graphs may also be defined geometrically, as the intersection graphs of line segments whose endpoints lie on two...

Chalopin, Jérémie; Gonçalves, Daniel (2009). "Every planar graph is the intersection graph of segments in the plane: extended abstract". In Mitzenmacher...

n\geq d+3} , so the class of graphs with bounded degeneracy has few cliques. Let G {\displaystyle G} be an intersection graph of n {\displaystyle n} convex...

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets...

nonempty intersection in H. In other words, L(H) is the intersection graph of a family of finite sets. It is a generalization of the line graph of a graph. Questions...

most n. The graph of the Erdős–Faber–Lovász conjecture may be represented as an intersection graph of sets: to each vertex of the graph, correspond the...

is, the clique graph K(G) is the intersection graph of the maximal cliques of G. A graph H is the clique graph K(G) of another graph if and only if there...