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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…
math.CO2020
Extending drawings of complete graphs into arrangements of pseudocircles
Alan Arroyo, R. Bruce Richter, Matthew Sunohara
Motivated by the successful application of geometry to proving the Harary-Hill Conjecture for "pseudolinear" drawings of , we introduce "pseudospherical" drawings of graphs. A…