Geometric graph theory

mathematical problem

In the mathematical field of graph theory, the boxicity of a graph is a graph invariant defined to be the minimum dimension of Euclidean space required to represent the graph as an intersection graph of axis-parallel closed boxes. That is, there must exist a one-to-one correspondence between the vertices of the graph and these boxes, such that two boxes intersect if and only if there is an edge connecting the corresponding vertices.

data structure to represent an embedding of a planar graph in the plane, and polytopes in 3D

type of graph theory

Characterizes graphs formed by edges and vertices of 3-dimensional convex polyhedra