### 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 language | English (US) |
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Pages (from-to) | 633-637 |

Number of pages | 5 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 34 |

DOIs | |

State | Published - Aug 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*34*, 633-637. https://doi.org/10.1016/j.endm.2009.07.107

}

*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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the Plane-Width of Graphs

AU - Kamiński, Marcin

AU - Medvedev, Paul

AU - Milanič, Martin

PY - 2009/8/1

Y1 - 2009/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=67651162013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67651162013&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2009.07.107

DO - 10.1016/j.endm.2009.07.107

M3 - Article

VL - 34

SP - 633

EP - 637

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -