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Space Crossing Numbers

Published online by Cambridge University Press:  16 March 2012

BORIS BUKH  and
ALFREDO HUBARD
BORIS BUKH
Affiliation:
DPMMS, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK and Churchill College, Cambridge CB3 0DS, UK (e-mail: B.Bukh@dpmms.cam.ac.uk)
ALFREDO HUBARD
Affiliation:
Courant Institute of Mathematical Sciences, New York University, NY 10012-1185, USA (e-mail: hubard@cims.nyu.edu)
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Abstract

We define a variant of the crossing number for an embedding of a graph G into ℝ3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the rectilinear space crossing numbers of pseudo-random graphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 3 , May 2012 , pp. 358 - 373
Copyright
Copyright © Cambridge University Press 2012

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