Marcus Kühn

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20212024

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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.CO2021

Fractional cycle decompositions in hypergraphs

Felix Joos, Marcus Kühn

We prove that for any integer $k \geq 2$ and $ε > 0$ , there is an integer $ℓ_{0} \geq 1$ such that any $k$ -uniform hypergraph on $n$ vertices with minimum codegree at least…