O. Solé-Pi

activity

20222026

collaborators

9 papers

math.CO2026

Crossing numbers of simplicial complexes

Alfredo Hubard, Cheikh Saliou Ndiaye, Oriol Solé-Pi

This paper studies crossing numbers of $d$ -dimensional simplicial complexes drawn in $R^{2 d}$ or $S^{2 d}$ . We clarify and generalize a number of known results and c…

math.CO2026

Uniform Geodesic Drawings of Graphs

Saba Lepsveridze, Oriol Solé-Pi

We study crossing numbers of dense graph drawings whose vertices are uniformly distributed either on the unit sphere or in a compact convex planar domain. We prove a sharp inequali…

math.CO2026

There are many 5-holes

Omar Astudillo-Marbán, Oriol Solé-Pi

Given a set P of points on the plane, a polygon with vertices in P is said to be empty if it contains no element of P in its interior. We show that every set of n points in general…

math.CO2025

Minor-excluded graphs and soficity

Oriol Solé-Pi

A random rooted graph is said to be sofic if it is the Benjamini-Schramm limit of a sequence of finite graphs. Given any finite graph $H$ , we prove that every one-ended, unimodular…

math.PR2025

Sharp threshold for network recovery from voter model dynamics

Hang Du, Seokmin Ha, Oriol Solé-Pi

We investigate the problem of recovering a latent directed Erdős-Rényi graph $G^{*} \sim G (n, p)$ from observations of discrete voter model trajectories on $G^{*}$ , where $n p$ g…

math.CO2025

On the crossing profile of rectilinear drawings of $K_{n}$

Isaac Chen, Oriol Solé-Pi

We introduce the \textit{crossing profile} of a drawing of a graph. This is a sequence of integers whose $(k + 1)^{th}$ entry counts the number of edges in the drawing which a…

math.CO2024

An algorithm for estimating the crossing number of dense graphs, and continuous analogs of the crossing and rectilinear crossing numbers

Oriol Solé-Pi

We present a deterministic $n^{2 + o (1)}$ -time algorithm that approximates the crossing number of any graph $G$ of order $n$ up to an additive error of $o (n^{4})$ . We also provide a ra…

math.CO2022

Crossing and intersecting families of geometric graphs on point sets

José Luis Álvarez-Rebollar, Jorge Cravioto-Lagos, Nestaly Marín +2

Let $S$ be a set of $n$ points in the plane in general position. Two line segments connecting pairs of points of $S$ cross if they have an interior point in common. Two vertex disj…

cs.CG2022

Optimal Placement of Base Stations in Border Surveillance using Limited Capacity Drones

S. Bereg, J. M. Díaz-Báñez, M. Haghpanah +8

Imagine an island modeled as a simple polygon $¶$ with $n$ vertices whose coastline we wish to monitor. We consider the problem of building the minimum number of refueling stations…

Crossing numbers of simplicial complexes

Uniform Geodesic Drawings of Graphs

There are many 5-holes

Minor-excluded graphs and soficity

Sharp threshold for network recovery from voter model dynamics

On the crossing profile of rectilinear drawings of Kn​

An algorithm for estimating the crossing number of dense graphs, and continuous analogs of the crossing and rectilinear crossing numbers

Crossing and intersecting families of geometric graphs on point sets

Optimal Placement of Base Stations in Border Surveillance using Limited Capacity Drones

On the crossing profile of rectilinear drawings of $K_{n}$