8 papers · 1 filter
Torsoids in Path-Like Graphs without nontrivial even 2-separation
Nathan Bowler, Florian Reich, Qiuzhenyu Tao
Bowler et al. introduced the concept of torsoids that describes the 1-separations of a directed graph in a canonical way building on previous progress by Lov{á}sz. To fully underst…
On the Possibilities of Defining Infinite Oriented Matroids
Nathan Bowler, Winfried Hochstättler, Stefan Kaspar
Is it possible to define cryptomorphic axiom systems for infinite oriented matroids by lifting some of the axiom systems for finite oriented matroids to the infinite setting while…
A structure theorem for rooted connectivity in bidirected graphs
Tara Abrishami, Nathan Bowler, Attila Joó +2
Recently, bidirected graphs have received increasing attention from the graph theory community with both structural and algorithmic results. Bidirected graphs are a generalization…
Hitting cycles through prescribed vertices or edges
Nathan Bowler, Ebrahim Ghorbani, Florian Gut +2
We prove that for every set of vertices of a directed graph , the maximum number of vertices in contained in a collection of vertex-disjoint cycles in is at least th…
Circuit-partition of infinite matroids
Nathan Bowler, Attila Joó
Komjáth, Milner, and Polat investigated when a finitary matroid admits a partition into circuits. They defined the class of ``finite matching extendable'' matroids and showed in th…
Connectoids II: existence of normal trees
Nathan Bowler, Florian Reich
In this series, we introduce and investigate the concept of connectoids, which captures the connectivity structure of various discrete objects such as undirected graphs, directed g…