### Abstract

Let G be a geometric graph with n vertices, i.e., a graph drawn in the plane with straight-line edges. It is shown that if G has no self-intersecting path of length 3, then its number of edges is O(n log n). This result is asymptotically tight. Analogous questions for curvilinear drawings and for longer paths are also considered.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 295-311 |

Number of pages | 17 |

Volume | 2528 LNCS |

Publication status | Published - 2002 |

Event | 10th International Symposium on Graph Drawing, GD 2002 - Irvine, CA, United States Duration: Aug 26 2002 → Aug 28 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2528 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th International Symposium on Graph Drawing, GD 2002 |
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Country | United States |

City | Irvine, CA |

Period | 8/26/02 → 8/28/02 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 2528 LNCS, pp. 295-311). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2528 LNCS).

**Geometric graphs with no self-intersecting path of length three.** / Pach, János; Pinchasi, Rom; Tardos, G.; Tóth, Géza.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 2528 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2528 LNCS, pp. 295-311, 10th International Symposium on Graph Drawing, GD 2002, Irvine, CA, United States, 8/26/02.

}

TY - GEN

T1 - Geometric graphs with no self-intersecting path of length three

AU - Pach, János

AU - Pinchasi, Rom

AU - Tardos, G.

AU - Tóth, Géza

PY - 2002

Y1 - 2002

N2 - Let G be a geometric graph with n vertices, i.e., a graph drawn in the plane with straight-line edges. It is shown that if G has no self-intersecting path of length 3, then its number of edges is O(n log n). This result is asymptotically tight. Analogous questions for curvilinear drawings and for longer paths are also considered.

AB - Let G be a geometric graph with n vertices, i.e., a graph drawn in the plane with straight-line edges. It is shown that if G has no self-intersecting path of length 3, then its number of edges is O(n log n). This result is asymptotically tight. Analogous questions for curvilinear drawings and for longer paths are also considered.

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M3 - Conference contribution

SN - 3540001581

SN - 9783540001584

VL - 2528 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 295

EP - 311

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -