A. Arroyo

activity

20152021

most citedConvex drawings of the complete graph: topology meets geometry

3 citations · 7 across the 10 of their papers we have counts for

collaborators

13 papers

cs.CG2021

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…

cs.CG2021

On Compatible Matchings

Oswin Aichholzer, Alan Arroyo, Zuzana Masárová +5

A matching is compatible to two or more labeled point sets of size $n$ with labels ${1, \dots, n}$ if its straight-line drawing on each of these point sets is crossing-free. We stu…

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 $cr (K_{n})$ of the complete graph $K_{n}$ in the plane (equivalently, the sphere) is $\frac{1}{4}\lfloor\frac{n}{2}\rfloor\lflo…

math.CO2020★ 2 cited

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 $K_{n}$ , we introduce "pseudospherical" drawings of graphs. A…

math.CO2019

The unavoidable rotation systems

Alan Arroyo, R. Bruce Richter, Gelasio Salazar +1

For each positive integer $m$ , Pach, Solymosi, and Tóth identified two canonical complete topological subgraphs $C_{m}$ and $T_{m}$ , and proved that every sufficiently large topologica…

cs.CG2019

Inserting one edge into a simple drawing is hard

Alan Arroyo, Fabian Klute, Irene Parada +3

A {\em simple drawing} $D (G)$ of a graph $G$ is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge $e$ in the complement o…

cs.CG2019

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…

math.CO2019★ 2 cited

Graphs with at most one crossing

André C. Silva, Alan Arroyo, R. Bruce Richter +1

The crossing number of a graph $G$ is the least number of crossings over all possible drawings of $G$ . We present a structural characterization of graphs with crossing number one.

math.CO2018

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…

math.CO2017★ 3 cited

Convex drawings of the complete graph: topology meets geometry

Alan Arroyo, Dan McQuillan, R. Bruce Richter +1

In this work, we introduce and develop a theory of convex drawings of the complete graph $K_{n}$ in the sphere. A drawing $D$ of $K_{n}$ is convex if, for every 3-cycle $T$ of $K_{n}$ , t…

math.CO2016

The crossing number of the cone of a graph

Carlos A. Alfaro, Alan Arroyo, Marek Derunár +1

Motivated by a problem asked by Richter and by the long standing Harary-Hill conjecture, we study the relation between the crossing number of a graph $G$ and the crossing number of…

math.CO2016

Drawings of Kn with the same rotation scheme are the same up to Reidemeister moves. Gioan's Theorem