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On the plane-width of graphs

par Kaminski, Marcin ;Medvedev, Paul;Milanic, Martin
Référence Electronic Notes in Discrete Mathematics, 34, page (633-637)
Publication Publié, 2009

Article révisé par les pairs

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Résumé :

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. © 2009 Elsevier B.V. All rights reserved.