4 papers · 1 filter
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…
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…
The unavoidable rotation systems
Alan Arroyo, R. Bruce Richter, Gelasio Salazar +1
For each positive integer , Pach, Solymosi, and Tóth identified two canonical complete topological subgraphs and , and proved that every sufficiently large topologica…
Extending Drawings of Graphs to Arrangements of Pseudolines
Alan Arroyo, Julien Bensmail, R. Bruce Richter
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two…