A characterization of planar graphs by pseudo-line arrangements

Hisao Tamaki, Takeshi Tokuyama

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

16 Citations (Scopus)

Abstract

Let G be an arrangement of pseudo-lines, i.e., a collection of unbounded x-monotone curves in which each curve crosses each of the others exactly once. A pseudo-line graph (G, E) is a graph for which the vertices are the pseudo-lines of G and the edges are some un-ordered pairs of pseudo-lines of G. A diamond of pseudo-line graph (G, E) is a pair of edges {p, q}, {pʹ, qʹ} ϵ E, {p, q} Ç {pʹ, qʹ} = ø, such that the crossing point of the pseudo-lines p and q lies vertically between pʹ and qʹ and the crossing point of pʹ and qʹ lies vertically between p and q. We show that a graph is planar if and only if it is isomorphic to a diamond-free pseudo-line graph. An immediate consequence of this theorem is that the O(kl/3n) upper bound on the k-level complexity of an arrangement of straightfines, which is very recently discovered by Dey, holds for an arrangement of pseudo-lines as well.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 8th International Symposium, ISAAC 1997, Proceedings
EditorsHon Wai Leong, Sanjay Jain, Hiroshi Imai
PublisherSpringer Verlag
Pages133-142
Number of pages10
ISBN (Print)3540638903, 9783540638902
DOIs
Publication statusPublished - 1997
Event8th Annual International Symposium on Algorithms and Computation, ISAAC 1997 - Singapore, Singapore
Duration: 1997 Dec 171997 Dec 19

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1350
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th Annual International Symposium on Algorithms and Computation, ISAAC 1997
Country/TerritorySingapore
CitySingapore
Period97/12/1797/12/19

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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