B. Schülke

activity

20192024

collaborators

Showing math.COShow all

8 papers · 1 filter

math.CO2024

Separating hypergraph Turán densities

Hong Liu, Bjarne Schülke, Shuaichao Wang +2

Determining the Turán densities of hypergraphs is a notoriously difficult problem at the core of combinatorics. Although Turán posed this problem in 1941, $π (K_{ℓ}^{(k)})$ remai…

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.CO2021

Decomposing hypergraphs into cycle factors

Felix Joos, Marcus Kühn, Bjarne Schülke

A famous result by Rödl, Ruciński, and Szemerédi guarantees a (tight) Hamilton cycle in $k$ -uniform hypergraphs $H$ on $n$ vertices with minimum $(k - 1)$ -degree $δ_{k-1}(H)\geq (1/2…

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

Minimum pair degree condition for tight Hamiltonian cycles in $4$ -uniform hypergraphs

Joanna Polcyn, Christian Reiher, Vojtěch Rödl +3

We show that every 4-uniform hypergraph with $n$ vertices and minimum pair degree at least $(5/9 + o (1)) n^{2} /2$ contains a tight Hamiltonian cycle. This degree condition is asymptotic…

math.CO2019

Short proof that Kneser graphs are Hamiltonian for $n \geq 4 k$

Johann Bellmann, Bjarne Schülke

For integers $n \geq k \geq 1$ , 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…