All four variants of the segment number are ∃R-complete to decide, and there exist planar graphs where the classical segment number is asymptotically twice the 3D, bend, or crossing variant.
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Variants of the Segment Number of a Graph
All four variants of the segment number are ∃R-complete to decide, and there exist planar graphs where the classical segment number is asymptotically twice the 3D, bend, or crossing variant.