B. Schülke

activity

20192021

collaborators

6 papers

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…

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…

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