### Abstract

It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmović, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.

Original language | English (US) |
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Pages (from-to) | 260-267 |

Number of pages | 8 |

Journal | Computational Geometry: Theory and Applications |

Volume | 48 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2015 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

### Keywords

- Degenerate drawing of a graph
- Distance number of a graph
- Outerplanar graphs

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## Cite this

Alon, N., & Feldheim, O. N. (2015). Drawing outerplanar graphs using three edge lengths.

*Computational Geometry: Theory and Applications*,*48*(3), 260-267. https://doi.org/10.1016/j.comgeo.2014.10.006