B. Schülke

activity

20192024

most citedMinimum pair degree condition for tight Hamiltonian cycles in

4

-uniform hypergraphs

5 citations · 5 across the 7 of their papers we have counts for

collaborators

8 papers

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★ 5 cited

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…

math.CO2019

Convex graphon parameters and graph norms

Joonkyung Lee, Bjarne Schülke

Sidorenko's conjecture states that the number of copies of a bipartite graph $H$ in a graph $G$ is asymptotically minimised when $G$ is a quasirandom graph. A notorious example whe…

math.CO2019

A pair degree condition for Hamiltonian cycles in $3$ -uniform hypergraphs

Bjarne Schülke

We prove a new sufficient pair degree condition for tight Hamiltonian cycles in $3$ -uniform hypergraphs that (asymptotically) improves the best known pair degree condition due to R…

Separating hypergraph Turán densities

The codegree Turán density of tight cycles minus one edge

Decomposing hypergraphs into cycle factors

r-cross t-intersecting families via necessary intersection points

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

Short proof that Kneser graphs are Hamiltonian for n≥4k

Convex graphon parameters and graph norms

A pair degree condition for Hamiltonian cycles in 3-uniform hypergraphs

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

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

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

A pair degree condition for Hamiltonian cycles in $3$ -uniform hypergraphs