### 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 language | English (US) |
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Pages (from-to) | 347-358 |

Number of pages | 12 |

Journal | Random Structures and Algorithms |

Volume | 21 |

Issue number | 3-4 |

State | Published - Oct 2002 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Random Structures and Algorithms*,

*21*(3-4), 347-358.

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

Research output: Contribution to journal › Article

*Random Structures and Algorithms*, vol. 21, no. 3-4, pp. 347-358.

}

TY - JOUR

T1 - Crossing Numbers of Random Graphs

AU - Spencer, Joel

AU - Tóth, Géza

PY - 2002/10

Y1 - 2002/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0242330697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242330697&partnerID=8YFLogxK

M3 - Article

VL - 21

SP - 347

EP - 358

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 3-4

ER -