Simón Piga

activity

20202026

most citedLocalised codegree conditions for tight Hamilton cycles in 3-uniform hypergraphs

3 citations · 7 across the 18 of their papers we have counts for

collaborators

18 papers

math.CO2026

Upper bounds on the running time of bootstrap percolation

Weichan Liu, Xiangxiang Nie, Simón 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 Hladký, Simón 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…

math.CO2025

On possible uniform Turán densities

Dylan King, Simón Piga, Marcelo Sales +1

Given a family of $3$ -graphs $F$ , the uniform Turán density $π_{∴} (F)$ is defined as the infimum $d \in [0, 1]$ for which any sufficiently large uniformly…

math.CO2024

Powers of Hamilton cycles in oriented and directed graphs

Louis DeBiasio, Jie Han, Allan Lo +3

The Pósa--Seymour conjecture determines the minimum degree threshold for forcing the $k$ th power of a Hamilton cycle in a graph. After numerous partial results, Komlós, Sárközy and…

math.CO2024

The codegree Turán density of $3$ -uniform tight cycles

Simón Piga, Nicolás 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…

math.CO2023

Simplicial Turán problems

David Conlon, Simón Piga, Bjarne Schülke

A simplicial complex $H$ consists of a pair of sets $(V, E)$ where $V$ is a set of vertices and $E \subseteq P (V)$ is a collection of subsets of $V$ closed under taking subs…

math.CO2023★ 1 cited

Hypergraphs with arbitrarily small codegree Turán density

Simón Piga, Bjarne Schülke

Let $k \geq 3$ . Given a $k$ -uniform hypergraph $H$ , the minimum codegree $δ (H)$ is the largest $d \in N$ such that every $(k - 1)$ -set of $V (H)$ is contained in at least $d$ ed…

math.CO2023

Tiling edge-ordered graphs with monotone paths and other structures

Igor Araujo, Simón Piga, Andrew Treglown +1

Given graphs $F$ and $G$ , a perfect $F$ -tiling in $G$ is a collection of vertex-disjoint copies of $F$ in $G$ that together cover all the vertices in $G$ . The study of the minimum…

math.CO2022

On oriented cycles in randomly perturbed digraphs

Igor Araujo, József Balogh, Robert A. Krueger +2

In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every $α > 0$ , there exists a constant $C$ such…

math.CO2022

The codegree Turán density of tight cycles minus one edge

Simón Piga, Marcelo Sales, Bjarne Schülke

Given $α > 0$ and an integer $ℓ \geq 5$ , we prove that every sufficiently large $3$ -uniform hypergraph $H$ on $n$ vertices in which every two vertices are contained in at least $α n$ …

math.CO2022

Cycle decompositions in $k$ -uniform hypergraphs

Allan Lo, Simón Piga, Nicolás Sanhueza-Matamala

We show that $k$ -uniform hypergraphs on $n$ vertices whose codegree is at least $(2/3 + o (1)) n$ can be decomposed into tight cycles, subject to the trivial divisibility conditions.…

math.CO2022★ 1 cited

Ramsey numbers with prescribed rate of growth

Matías Pavez-Signé, Simón Piga, Nicolás Sanhueza-Matamala

Let $R (G)$ be the two-colour Ramsey number of a graph $G$ . In this note, we prove that for any non-decreasing function $n \leq f (n) \leq R (K_{n})$ , there exists a sequence of connect…

math.CO2022

The induced saturation problem for posets

Andrea Freschi, Simón Piga, Maryam Sharifzadeh +1

For a fixed poset $P$ , a family $F$ of subsets of $[n]$ is induced $P$ -saturated if $F$ does not contain an induced copy of $P$ , but for every subset $S$ of $[n]$ …

math.CO2022

Turán density of cliques of order five in $3$ -uniform hypergraphs with quasirandom links

Sören Berger, Simón Piga, Christian Reiher +2

We show that $3$ -uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than $1/3$ contain a clique on five vertices. This result…

math.CO2021★ 2 cited

Cycle decompositions in $3$ -uniform hypergraphs

Simón Piga, Nicolás Sanhueza-Matamala

We show that $3$ -graphs on $n$ vertices whose codegree is at least $(2/3 + o (1)) n$ can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divis…

math.CO2020

$r$ -cross $t$ -intersecting families via necessary intersection points

Pranshu Gupta, Yannick Mogge, Simón Piga +1

Given integers $r \geq 2$ and $n, t \geq 1$ we call families $F_{1}, \dots, F_{r} \subseteq P ([n])$ $r$ -cross $t$ -intersecting if for all $F_{i} \in F_{i}$ ,…

math.CO2020

On extremal problems concerning the traces of sets

Simón Piga, Bjarne Schülke

Given two non-negative integers $n$ and $s$ , define $m (n, s)$ to be the maximal number such that in every hypergraph $H$ on $n$ vertices and with at most $m (n, s)$ edges t…

math.CO2020★ 3 cited

Localised codegree conditions for tight Hamilton cycles in 3-uniform hypergraphs

Pedro Araújo, Simón Piga, Mathias Schacht

We study sufficient conditions for the existence of Hamilton cycles in uniformly dense $3$ -uniform hypergraphs. Problems of this type were first considered by Lenz, Mubayi, and Myc…

Upper bounds on the running time of bootstrap percolation

Hamiltonicity of inhomogeneous random graphs

On possible uniform Turán densities

Powers of Hamilton cycles in oriented and directed graphs

The codegree Turán density of 3-uniform tight cycles

Simplicial Turán problems

Hypergraphs with arbitrarily small codegree Turán density

Tiling edge-ordered graphs with monotone paths and other structures

On oriented cycles in randomly perturbed digraphs

The codegree Turán density of tight cycles minus one edge

Cycle decompositions in k-uniform hypergraphs

Ramsey numbers with prescribed rate of growth

The induced saturation problem for posets

Turán density of cliques of order five in 3-uniform hypergraphs with quasirandom links

Cycle decompositions in 3-uniform hypergraphs

r-cross t-intersecting families via necessary intersection points

On extremal problems concerning the traces of sets

Localised codegree conditions for tight Hamilton cycles in 3-uniform hypergraphs

The codegree Turán density of $3$ -uniform tight cycles

Cycle decompositions in $k$ -uniform hypergraphs

Turán density of cliques of order five in $3$ -uniform hypergraphs with quasirandom links

Cycle decompositions in $3$ -uniform hypergraphs

$r$ -cross $t$ -intersecting families via necessary intersection points