  Map vertices of a graph to (not necessarily distinct) points of the plane so
that two adjacent vertices are mapped at least a unit distance apart. The
plane-width of a graph is the minimum diameter of the image of the vertex set
over all such mappings. We establish a relation between the plane-width of a
graph and its chromatic number, and connect it to other well-known areas,
including the circular chromatic number and the problem of packing unit discs
in the plane. We also investigate how plane-width behaves under various
operations, such as homomorphism, disjoint union, complement, and the Cartesian
product.
