66 citations · 77 across the 14 of their papers we have counts for
16 papers
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…
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…
Graphs with at most one crossing
André C. Silva, Alan Arroyo, R. Bruce Richter +1
The crossing number of a graph is the least number of crossings over all possible drawings of . We present a structural characterization of graphs with crossing number one.
Bounding the number of non-duplicates of the -side in simple drawings of
R. Bruce Richter, André C. Silva, Orlando Lee
The number is the smallest number of crossings in a simple planar drawing of in which both vertices on the 2-side have th…