Geometric graphs with no self-intersecting path of length three

János Pach, Rom Pinchasi, G. Tardos, Géza Tóth

Research output: Contribution to journalArticle

7 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(nlogn). This result is asymptotically tight. Analogous questions for longer forbidden paths and for graphs drawn by not necessarily straight-line edges are also considered.

Original languageEnglish
Pages (from-to)793-811
Number of pages19
JournalEuropean Journal of Combinatorics
Volume25
Issue number6
DOIs
Publication statusPublished - Aug 2004

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Geometric Graphs
Straight Line
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Graph in graph theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

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

In: European Journal of Combinatorics, Vol. 25, No. 6, 08.2004, p. 793-811.

Research output: Contribution to journalArticle

Pach, János ; Pinchasi, Rom ; Tardos, G. ; Tóth, Géza. / Geometric graphs with no self-intersecting path of length three. In: European Journal of Combinatorics. 2004 ; Vol. 25, No. 6. pp. 793-811.
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