B. Schulke

activity

20192026

collaborators

10 papers

math.CO2026

Bootstrap percolation of extension hypergraphs

Weichan Liu, Bjarne Schülke, Xin Zhang

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.CO2025

Hypergraphs accumulate infinitely often

David Conlon, Bjarne Schülke

We show that the set $Π^{(k)}$ of Turán densities of $k$ -uniform hypergraphs has infinitely many accumulation points in $[0, 1)$ for every $k \geq 3$ . This extends an earlier result…

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.CO2025

Infinitely many accumulation points of codegree Turán densities

Heng Li, Weichan Liu, Bjarne Schülke +1

The codegree Turán density $γ (F)$ of a $k$ -graph $F$ is the smallest $γ \in [0, 1)$ such that every $k$ -graph $H$ with $δ_{k - 1} (H) \geq (γ + o (1)) ∣ V (H) ∣$ contains a copy of $F$ .…

math.CO2025

Minimum degree in simplicial complexes

Christian Reiher, Bjarne Schülke

Given $d \in N$ , let $α (d)$ be the largest real number such that every abstract simplicial complex $S$ with $0<\vert\mathcal{S}\vert\leqα(d)\vert V(\mathcal{S})\ve…

math.CO2024

Lagrangians are attained as uniform Turán densities

Dylan King, Marcelo Sales, Bjarne Schülke

The study of uniform Turán densities was initiated in the 1980s by Erdős and Sós. Given a $3$ -graph $F$ , the uniform Turán density of $F$ , $π_{∴} (F)$ , is defined as the in…

math.CO2024

Hypergraphs accumulate

David Conlon, Bjarne Schülke

We show that for every integer $k \geq 3$ , the set of Turán densities of $k$ -uniform hypergraphs has an accumulation point in $[0, 1)$ . In particular, $1/2$ is an accumulation point f…

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.CO2022

A local version of Katona's intersection theorem

Marcelo Sales, Bjarne Schülke

Katona's intersection theorem states that every intersecting family $F \subseteq [n]^{(k)}$ satisfies $∣ \partial F ∣ \geq ∣ F ∣$ , where $\partial…

math.CO2019

Clique factors in Kneser graphs

Johann Bellmann, Bjarne Schülke

For $k, n \in N$ , the Kneser graph $K (n, k)$ is the graph with vertex set $V = [n]^{(k)}$ and edge set $E = {{x, y} \in V^{(2)} : x \cap y = \emptyset}$ . Chen proved that for $n\g…