Simón Piga

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20242026

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5 papers · 1 filter

math.CO2026

Upper bounds on the running time of bootstrap percolation

Weichan Liu, Xiangxiang Nie, SimÃ³n Piga +1

For $k$ -graphs $F$ and $H_{0}$ the $F$ -bootstrap percolation process (or $F$ -process) starting with $H_{0}$ is a sequence $(H_{i})_{i \geq 0}$ of $k$ -graphs such that $H_{i + 1}$ is obtained…

math.CO2026

Hamiltonicity of inhomogeneous random graphs

Frederik Garbe, Jan HladkÃ½, SimÃ³n Piga

We provide a complete characterization of those graphons $W$ for which the inhomogeneous random graph $G (n, W)$ is asymptotically almost surely Hamiltonian. The characterization inv…

math.CO2025

Powers of Hamilton cycles in oriented and directed graphs

Louis DeBiasio, Jie Han, Allan Lo +3

The PÃ³sa--Seymour conjecture determines the minimum degree threshold for forcing the $k$ th power of a Hamilton cycle in a graph. After numerous partial results, KomlÃ³s, SÃ¡rkÃ¶zy…

math.CO2025

On possible uniform TurÃ¡n densities

Dylan King, SimÃ³n Piga, Marcelo Sales +1

Given a family of $3$ -graphs $F$ , the uniform TurÃ¡n density $I ¨ _{∴} (F)$ is defined as the infimum $d \in [0, 1]$ for which any sufficiently large uniform…

math.CO2024

The codegree TurÃ¡n density of $3$ -uniform tight cycles

SimÃ³n Piga, NicolÃ¡s Sanhueza-Matamala, Mathias Schacht

Given any $ε > 0$ we prove that every sufficiently large $n$ -vertex $3$ -graph $H$ where every pair of vertices is contained in at least $(1/3 + ε) n$ edges contains…