The Pach-Spencer-Tóth conjecture on optimal crossing lower bounds for graphs with sparse subgraphs is proved, and the admissible degree-sum range for the bisection-width bound is fully determined.
Ackerman, On topological graphs with at most four crossings per edge, Computa- tional Geometry 85 (2019), 35 pages
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On a conjecture of Pach-Spencer-T\'oth for graph crossing numbers
The Pach-Spencer-Tóth conjecture on optimal crossing lower bounds for graphs with sparse subgraphs is proved, and the admissible degree-sum range for the bisection-width bound is fully determined.