A Crossing Lemma for the pair-crossing number

Eyal Ackerman; Marcus Schaefer

doi:10.1007/978-3-662-45803-7_19

A Crossing Lemma for the pair-crossing number

Eyal Ackerman, Marcus Schaefer

Faculty of Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The pair-crossing number of a graph G, pcr(G), is the minimum possible number of pairs of edges that cross each other (possibly several times) in a drawing of G. It is known that there is a constant c ≥ 1/64 such that for every (not too sparse) graph G with n vertices and m edges pcr(G) ≥ c m³/n². This bound is tight, up to the constant c. Here we show that c ≥ 1/34.2 if G is drawn without adjacent crossings.

Original language	English
Pages (from-to)	222-233
Number of pages	12
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8871
DOIs	https://doi.org/10.1007/978-3-662-45803-7_19
State	Published - 2014

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2014.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-662-45803-7_19

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A Crossing Lemma for the pair-crossing number

Abstract

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