On the Plane-Width of Graphs

Marcin Kamiński, Paul Medvedev, Martin Milanič

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)633-637
Number of pages5
JournalElectronic Notes in Discrete Mathematics
Volume34
DOIs
StatePublished - Aug 1 2009

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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