1 citations · 4 across the 10 of their papers we have counts for
11 papers
Maker-Breaker games on infinite graphs with precolored edges
Nathan Bowler, Florian Gut, Henri Ortmüller
Suppose we are given graphs and . In the classical Maker-Breaker game two players, Maker and Breaker, alternately claim edges of and it is Maker's goal…
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…
The -Game
Nathan Bowler, Florian Gut
We investigate a two player game called the -building game: two players alternately claim edges of an infinite complete graph. Each player's aim is to claim all six edges on s…
The Rational Number Game
Nathan Bowler, Florian Gut
We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately cla…
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…
Maker-Breaker games on and
Nathan Bowler, Florian Gut, Attila Joó +1
We investigate Maker-Breaker games on graphs of size in which Maker's goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the gam…
Large vertex-flames in uncountable digraphs
Florian Gut, Attila Joó
The study of minimal subgraphs witnessing a connectivity property is an important field in graph theory. The foundation for large flames has been laid by Lovász: Let be…
The Game: Vertex Colouring
Nathan Bowler, Marit Emde, Florian Gut
We investigate games played between Maker and Breaker on an infinite complete graph whose vertices are coloured with colours from a given set, each colour appearing infinitely ofte…