Marc Kaufmann

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3 papers · 1 filter

math.CO2025

Sharp Thresholds for Factors in Random Graphs

Fabian Burghart, Annika Heckel, Marc Kaufmann +2

Let $F$ be a graph on $r$ vertices and let $G$ be a graph on $n$ vertices. Then an $F$ -factor in $G$ is a subgraph of $G$ composed of $n / r$ vertex-disjoint copies of $F$ , if $r$ di…

math.CO2024

The hitting time of nice factors

Fabian Burghart, Marc Kaufmann, Noela MÃ¼ller +1

Consider the random $u$ -uniform hypergraph (or $u$ -graph) process on $n$ vertices, where $n$ is divisible by $r > u \geq 2$ . It was recently shown that with high probability, as soon a…

math.CO2024

Heritability of KÅnig's Property from finite edge sets

Marc Kaufmann, Dominic van der Zypen

A hypergraph $H = (V, E)$ is said to have KÅnig's Property if there is a matching $M \subseteq E$ and $S \subseteq V$ such that $∣ S \cap e ∣ = 1$ for all $e \in M$ , and $S$ is a vertex…

Sharp Thresholds for Factors in Random Graphs

The hitting time of nice factors

Heritability of KÅnig's Property from finite edge sets

Heritability of KÅnig's Property from finite edge sets