### Abstract

Let S be any set of N points in the plane and let DT(S) be the graph of the Delaunay triangulation of S. For all points a and b of S, let d(a, b) be the Euclidean distance from a to b and let DT(a, b) be the length of the shortest path in DT(S) from a to b. We show that there is a constant c (≤((1+√5)/2) π≈5.08) independent of S and N such that {Mathematical expression}

Original language | English (US) |
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Pages (from-to) | 399-407 |

Number of pages | 9 |

Journal | Discrete & Computational Geometry |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1990 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Dobkin, D. P., Friedman, S. J., & Supowit, K. J. (1990). Delaunay graphs are almost as good as complete graphs.

*Discrete & Computational Geometry*,*5*(1), 399-407. https://doi.org/10.1007/BF02187801