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A generalisation of Menger's theorem in bidirected graphs
Ebrahim Ghorbani, Jana Katharina Nickel, Florian Reich
Menger's theorem - the maximum number of vertex-disjoint - paths is equal to the minimum size of an - separator - is generally not true in bidirected graphs. We prove t…
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…
On the ubiquity of oriented double rays
Florian Gut, Thilo Krill, Florian Reich
A digraph is called ubiquitous if every digraph that contains arbitrarily many vertex-disjoint copies of also contains infinitely many vertex-disjoint copies of . We stu…
Menger's Theorem in bidirected graphs
Nathan Bowler, Ebrahim Ghorbani, Florian Gut +2
Bidirected graphs are a generalisation of directed graphs that arises in the study of undirected graphs with perfect matchings. Menger's famous theorem - the minimum size of a set…
Decomposition of (infinite) digraphs along directed 1-separations
Nathan Bowler, Florian Gut, Meike Hatzel +3
We introduce torsoids, a canonical structure in matching covered graphs, corresponding to the bricks and braces of the graph. This allows a more fine-grained understanding of the s…
Ubiquity of oriented rays
Florian Gut, Thilo Krill, Florian Reich
Call a digraph \emph{ubiquitous} if every digraph that contains vertex-disjoint copies of for every also contains infinitely many vertex-disjoint…