The Plane-Width of Graphs
Discrete Mathematics
2013-01-08 v1
Abstract
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.
Cite
@article{arxiv.0812.4346,
title = {The Plane-Width of Graphs},
author = {Marcin Kaminski and Paul Medvedev and Martin Milanic},
journal= {arXiv preprint arXiv:0812.4346},
year = {2013}
}