Space crossing numbers
Boris Bukh, Alfredo Hubard

TL;DR
This paper introduces a new concept of crossing number for graph embeddings in three-dimensional space, establishes a lower bound related to the classical crossing lemma, and provides sharp bounds for pseudo-random graphs.
Contribution
It defines space crossing numbers, derives a near-classical lower bound, and determines sharp bounds for pseudo-random graphs, advancing understanding of graph embeddings in 3D.
Findings
Lower bound on space crossing number almost implies crossing lemma
Sharp bounds on space crossing numbers of pseudo-random graphs
Extension of crossing number concepts to 3D embeddings
Abstract
We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the space crossing numbers of pseudo-random graphs.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research
