Marc Kaufmann

collaborators

5 papers

math.CO2024

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 Müller +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 Kőnig's Property from finite edge sets

Marc Kaufmann, Dominic van der Zypen

A hypergraph $H = (V, E)$ is said to have Kőnig'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…

math.CO2023

Size-Ramsey numbers of structurally sparse graphs

Nemanja Draganić, Marc Kaufmann, David Munhá Correia +2

Size-Ramsey numbers are a central notion in combinatorics and have been widely studied since their introduction by Erdős, Faudree, Rousseau and Schelp in 1978. Research has mainly…

math.CO2023

The hitting time of clique factors

Annika Heckel, Marc Kaufmann, Noela Müller +1

In a recent paper, Kahn gave the strongest possible, affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let $r \geq 3$ and let $n$ be divisible by $…