### Abstract

Let G be a graph without loops or multiple edges drawn in the plane. It is shown that, for any k, if G has at least C_{k}n edges and n vertices, then it contains three sets of k edges, such that every edge in any of the sets crosses all edges in the other two sets. Furthermore, two of the three sets can be chosen such that all k edges in the set have a common vertex.

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 | 184-197 |

Number of pages | 14 |

Volume | 3742 LNCS |

DOIs | |

Publication status | Published - 2005 |

Event | Japanese Conference on Discrete and Computational Geometry, JCDCG 2004 - Tokyo, Japan Duration: Oct 8 2004 → Oct 11 2004 |

### 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 | 3742 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | Japanese Conference on Discrete and Computational Geometry, JCDCG 2004 |
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Country | Japan |

City | Tokyo |

Period | 10/8/04 → 10/11/04 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 3742 LNCS, pp. 184-197). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3742 LNCS). https://doi.org/10.1007/11589440_19

**Crossing stars in topological graphs.** / 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. 3742 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3742 LNCS, pp. 184-197, Japanese Conference on Discrete and Computational Geometry, JCDCG 2004, Tokyo, Japan, 10/8/04. https://doi.org/10.1007/11589440_19

}

TY - GEN

T1 - Crossing stars in topological graphs

AU - Tardos, G.

AU - Tóth, Géza

PY - 2005

Y1 - 2005

N2 - Let G be a graph without loops or multiple edges drawn in the plane. It is shown that, for any k, if G has at least Ckn edges and n vertices, then it contains three sets of k edges, such that every edge in any of the sets crosses all edges in the other two sets. Furthermore, two of the three sets can be chosen such that all k edges in the set have a common vertex.

AB - Let G be a graph without loops or multiple edges drawn in the plane. It is shown that, for any k, if G has at least Ckn edges and n vertices, then it contains three sets of k edges, such that every edge in any of the sets crosses all edges in the other two sets. Furthermore, two of the three sets can be chosen such that all k edges in the set have a common vertex.

UR - http://www.scopus.com/inward/record.url?scp=33646508782&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646508782&partnerID=8YFLogxK

U2 - 10.1007/11589440_19

DO - 10.1007/11589440_19

M3 - Conference contribution

SN - 3540304673

SN - 9783540304678

VL - 3742 LNCS

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

SP - 184

EP - 197

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

ER -