Crossing Numbers of Random Graphs

Joel Spencer, Géza Tóth

Research output: Contribution to journalArticle

Abstract

The crossing number of G is the minimum number of crossing points in any drawing of G. We consider the following two other parameters. The rectilinear crossing number is the minimum number of crossing points in any drawing of G, with straight line segments as edges. The pairwise crossing number of G is the minimum number of pairs of crossing edges over all drawings of G. We prove several results on the expected values of these parameters of a random graph.

Original languageEnglish (US)
Pages (from-to)347-358
Number of pages12
JournalRandom Structures and Algorithms
Volume21
Issue number3-4
StatePublished - Oct 2002

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Crossing number
Random Graphs
Line segment
Expected Value
Straight Line
Pairwise
Drawing

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Mathematics(all)
  • Applied Mathematics

Cite this

Crossing Numbers of Random Graphs. / Spencer, Joel; Tóth, Géza.

In: Random Structures and Algorithms, Vol. 21, No. 3-4, 10.2002, p. 347-358.

Research output: Contribution to journalArticle

Spencer, J & Tóth, G 2002, 'Crossing Numbers of Random Graphs', Random Structures and Algorithms, vol. 21, no. 3-4, pp. 347-358.
Spencer, Joel ; Tóth, Géza. / Crossing Numbers of Random Graphs. In: Random Structures and Algorithms. 2002 ; Vol. 21, No. 3-4. pp. 347-358.
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