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math.CO2026
Smallest Cubic Non-1-Planar Graphs
Sergey Pupyrev
A graph is 1-planar if it has a drawing in which every edge is crossed at most once. We show that the smallest cubic non-1-planar graphs have vertices. Two such graphs are the…
cs.DM2026
A Gap in the 42-Queue Layout Algorithm for Planar Graphs
Sergey Pupyrev
A queue layout of a graph consists of a linear order of the vertices and a partition of the edges into queues so that no two edges in a single queue are nested. The minimum number…
cs.CG2026
How to Draw a Planar Graph: An Experimental Evaluation
Sergey Pupyrev
Planar graphs are central to graph drawing, with extensive results on planar layouts and related structures. Every planar graph admits a planar straight-line drawing, and algorithm…