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math.CO2020
Remarks on the structure of simple drawings of
R. Bruce Richter, Matthew Sullivan
In studying properties of simple drawings of the complete graph in the sphere, two natural questions arose for us: can an edge have multiple segments on the boundary of the same fa…
math.CO2020
Drawings of complete graphs in the projective plane
Alan Arroyo, Dan McQuillan, R. Bruce Richter +2
Hill's Conjecture states that the crossing number of the complete graph in the plane (equivalently, the sphere) is $\frac{1}{4}\lfloor\frac{n}{2}\rfloor\lflo…