Maximilian Krone

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math.CO2025

Sufficient average degree conditions for the existence of large highly connected subgraphs

Maximilian Krone

Mader proved that every sufficiently large graph with average degree at least $(2 + 2) k$ has a $(k + 1)$ -connected subgraph. He also conjectured that an average degree of at lea…

math.CO2025

Sufficient minimum degree conditions for the existence of highly connected or edge-connected subgraphs

Maximilian Krone

Mader conjectured in 1979 that an average degree of at least $3 k - 1$ in a graph is sufficient for the existence of a $(k + 1)$ -connected subgraph. The following minimum degree analogu…

math.CO2024

Cut covers of acyclic digraphs

Maximilian Krone

A cut in a digraph $D = (V, A)$ is a set of arcs ${uv \in A : u \in U, v \in / U}$ , for some $U \subseteq V$ . It is known that the arc set $A$ is covered by $k$ cuts if and only if it…

math.CO2024

On an acyclic relaxation of incomparable families of sets

Maximilian Krone

For two families $A, B \subseteq P ([k])$ , we write $A ⊢ B$ if $A \neq \supseteq B$ for each two sets $A \in A$ and $B \…