B. Schulke

activity

20242026

collaborators

7 papers

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

Bootstrap percolation of extension hypergraphs

Weichan Liu, Bjarne SchÃ¼lke, 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.CO2026

Infinitely many accumulation points of codegree TurÃ¡n densities

Heng Li, Weichan Liu, Bjarne SchÃ¼lke +1

The codegree TurÃ¡n density $I^^{3} (F)$ of a $k$ -graph $F$ is the smallest $I^^{3} \in [0, 1)$ such that every $k$ -graph $H$ with $I^´_{k - 1} (H) \geq (I^^{3} + o (1)) ∣ V (H) ∣$ contains a copy of…

math.CO2025

Hypergraphs accumulate infinitely often

David Conlon, Bjarne SchÃ¼lke

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

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.CO2025

Minimum degree in simplicial complexes

Christian Reiher, Bjarne SchÃ¼lke

Given $d \in N$ , let $I^\pm (d)$ be the largest real number such that every abstract simplicial complex $S$ with $0<\vert\mathcal{S}\vert\leqÎ±(d)\vert V(\mathcal{S})\…