6 papers
Approximating the Bundled Crossing Number
Alan Arroyo, Stefan Felsner
Bundling crossings is a strategy which can enhance the readability of drawings. In this paper we consider good drawings, i.e., we require that any two edges have at most one common…
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 Simple Drawings
Alan Arroyo, Martin Derka, Irene Parada
Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extend…
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…