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An example of how intersecting sets define a 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 classes of graphs can be defined by the types of sets that are used to form an intersection representation of them.
2. The block graph of a graph G is another graph whose vertices are the blocks of G, with an edge connecting two vertices when the corresponding blocks share an articulation point; that is, it is the intersection graph of the blocks of G. The block graph of any graph is a forest. 3.
The midpoints on the three sides of these points of intersection are ... a collinearity graph of P is a ... Another way to say this is that the line segments joining ...
The intersection number of the graph is the smallest number such that there exists a representation of this type for which the union of the sets in has elements. [1] The problem of finding an intersection representation of a graph, using a given number of elements, is known as the intersection graph basis problem. [10]
We say that intersects (meets) if there exists some that is an element of both and , in which case we also say that intersects (meets) at. Equivalently, A {\displaystyle A} intersects B {\displaystyle B} if their intersection A ∩ B {\displaystyle A\cap B} is an inhabited set , meaning that there exists some x {\displaystyle x} such that x ∈ ...
For example, if manifolds of complementary dimension intersect transversally, the signed sum of the number of their intersection points does not change even if we isotope the manifolds to another transverse intersection. (The intersection points can be counted modulo 2, ignoring the signs, to obtain a coarser invariant.) This descends to a ...
A graph with 6 vertices and 7 edges. In mathematics and 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 is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).
There will be an intersection if 0 ≤ t ≤ 1 and 0 ≤ u ≤ 1. The intersection point falls within the first line segment if 0 ≤ t ≤ 1, and it falls within the second line segment if 0 ≤ u ≤ 1. These inequalities can be tested without the need for division, allowing rapid determination of the existence of any line segment ...