Maximilian Krone

works on

edge connectivity 1 graph connectivity 1 graph decomposition 1 minimum degree conditions 1 subgraph structure 1 triangle-free graphs 1

From the 1 of 4 linked papers with an AI index.

activity

20242026

collaborators

4 papers

math.CO2026

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

Maximilian Krone

The paper establishes sharp minimum-degree and average-degree thresholds that guarantee the existence of highly (k+1)-connected or (k+1)-edge-connected subgraphs, and applies these…

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

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 \…

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…