On the Plane-Width of Graphs

Marcin Kamiński, Paul Medvedev, Martin Milanič

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

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Graph in graph theory
Circular Chromatic number
Vertex of a graph
Chromatic number
Unit Disk
Packing
Adjacent
Distinct
Unit

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Kamiński, Marcin ; Medvedev, Paul ; Milanič, Martin. / On the Plane-Width of Graphs. In: Electronic Notes in Discrete Mathematics. 2009 ; Vol. 34. pp. 633-637.
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Kamiński, M, Medvedev, P & Milanič, M 2009, 'On the Plane-Width of Graphs', Electronic Notes in Discrete Mathematics, vol. 34, pp. 633-637. https://doi.org/10.1016/j.endm.2009.07.107

On the Plane-Width of Graphs. / Kamiński, Marcin; Medvedev, Paul; Milanič, Martin.

In: Electronic Notes in Discrete Mathematics, Vol. 34, 01.08.2009, p. 633-637.

Research output: Contribution to journalArticle

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