3 papers
math.CO2024
Augmenting a hypergraph to have a matroid-based -bounded -limited packing of rooted hypertrees
Pierre Hoppenot, Zoltán Szigeti
The aim of this paper is to further develop the theory of packing trees in a graph. We first prove the classic result of Nash-Williams \cite{NW} and Tutte \cite{Tu} on packing span…
math.CO2024
On arborescence packing augmentation in hypergraphs
Pierre Hoppenot, Zoltán Szigeti
We deepen the link between two classic areas of combinatorial optimization: augmentation and packing arborescences. We consider the following type of questions: What is the minimum…
math.CO2023
On reversing arcs to improve arc-connectivity
Pierre Hoppenot, Zoltán Szigeti
We show that if the arc-connectivity of a directed graph is at most and the reorientation of an arc set in results in a -arc-connected…