Thilo Hartel

collaborators

3 papers

math.CO2026

Cyclic Neighborhoods in Digraphs

Thilo Hartel, Dieter Rautenbach

Let $D$ be a digraph of order $n$ and size $m$ with the property that no out-neighborhood or in-neighborhood of any vertex is acyclic. We show that, if $D$ is strongly connected, t…

math.CO2026

Degenerate Vertex Cuts in Sparse Graphs

Thilo Hartel, Johannes Rauch, Dieter Rautenbach

For a non-negative integer $k$ , a vertex cut in a graph is $k$ -degenerate if it induces a $k$ -degenerate subgraph. We show that a graph of order $n$ at least $2 k + 2$ without a $k$ -d…

math.CO2025

On the number of maximal independent sets and maximal induced bipartite subgraphs in $K_{4}$ -free graphs

Thilo Hartel, Lucas Picasarri-Arrieta, Dieter Rautenbach

Let $G$ be a $K_{4}$ -free graph of order $n$ and let $k$ be an integer with $0 \leq k \leq n$ . We show the existence of positive constants $η$ and $ν$ such that $G$ has at most $(4-η)^…

Cyclic Neighborhoods in Digraphs

Degenerate Vertex Cuts in Sparse Graphs

On the number of maximal independent sets and maximal induced bipartite subgraphs in K4​-free graphs

On the number of maximal independent sets and maximal induced bipartite subgraphs in $K_{4}$ -free graphs