Geometric graphs with no self-intersecting path of length three

János Pach, Rom Pinchasi, G. 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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages295-311
Number of pages17
Volume2528 LNCS
Publication statusPublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Geometric Graphs
Longest Path
Straight Line
Path
Graph in graph theory
Drawing

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Pach, J., Pinchasi, R., Tardos, G., & Tóth, G. (2002). Geometric graphs with no self-intersecting path of length three. In 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2528 LNCS 2002. p. 295-311 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2528 LNCS).

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

Pach, J, Pinchasi, R, Tardos, G & Tóth, G 2002, Geometric graphs with no self-intersecting path of length three. in 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.
Pach J, Pinchasi R, Tardos G, Tóth G. Geometric graphs with no self-intersecting path of length three. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2528 LNCS. 2002. p. 295-311. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Pach, János ; Pinchasi, Rom ; Tardos, G. ; Tóth, Géza. / Geometric graphs with no self-intersecting path of length three. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2528 LNCS 2002. pp. 295-311 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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