What is "boxicity"

In graph theory, boxicity is a graph invariant, introduced by Fred S. Roberts in 1969.

The boxicity of a graph is the minimum dimension in which a given graph can be represented as an intersection graph of axis-parallel boxes. That is, there must exist a one-to-one correspondence between the vertices of the graph and a set of boxes, such that two boxes intersect if and only if there is an edge connecting the corresponding vertices.