### 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 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Kamiński, M., Medvedev, P., & Milanič, M. (2009). On the Plane-Width of Graphs.

*Electronic Notes in Discrete Mathematics*,*34*, 633-637. https://doi.org/10.1016/j.endm.2009.07.107