Geometric graphs with no self-intersecting path of length three

János Pach, Rom Pinchasi, Gabor Tardos, Géza Tóth

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

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 languageEnglish
Title of host publicationGraph Drawing - 10th International Symposium, GD 2002, Revised Papers
Pages295-311
Number of pages17
Publication statusPublished - Dec 1 2002
Event10th International Symposium on Graph Drawing, GD 2002 - Irvine, CA, United States
Duration: Aug 26 2002Aug 28 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2528 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Symposium on Graph Drawing, GD 2002
CountryUnited States
CityIrvine, CA
Period8/26/028/28/02

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Pach, J., Pinchasi, R., Tardos, G., & Tóth, G. (2002). Geometric graphs with no self-intersecting path of length three. In Graph Drawing - 10th International Symposium, GD 2002, Revised Papers (pp. 295-311). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2528 LNCS).