The aim of the REU, initiated by Miklós Abért, Péter Pál Pach and Dömötör Pálvölgyi in 2020, is to offer research opportunities to Hungarian math students during the summer. The participants are divided into smaller groups, and then they work together for one month on problems posed by senior researchers. For this year’s topics, see…
Consider a matroid equipped with a labeling of its ground set to an abelian group, and define the label of a subset of the ground set as the sum of the labels of its elements. In our paper Problems on group-labeled matroid bases, we study a collection of problems on finding bases and common bases…
In our paper titled Hypergraph connectivity augmentation in strongly polynomial time, we consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. The central theme of our work is to show that certain hypergraph network design problems admit solutions in which the number of hyperedges is polynomial…
Our paper on regular matroids has been accepted to the 56th Annual ACM Symposium on Theory of Computing (STOC 2024)! The paper provides an upper bound on the exchange distance of basis pairs in regular matroids. As a byproduct, we also verify a conjecture of Gabow from 1976 on the serial symmetric exchange property of…
A classical theorem of Nash-Williams implies that every $2k$-edge-connected graph has a $k$-arc-connected orientation. In 1985, Thomassen asked whether a similar statement is true for vertex-connectivity, and formulated a conjecture stating that for every positive integer $k$ there exists a smallest integer $f(k)$ such that every $f(k)$-connected graph has a $k$-connected orientation. In a recent…