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arXiv · 0812.4346

The Plane-Width of Graphs

Marcin Kaminski·Paul Medvedev·Martin Milanic
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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.

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Marcin Kaminski, Paul Medvedev, Martin Milanic. 2008-12-23. The Plane-Width of Graphs. https://doi.org/10.1002/jgt.20554

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