7 papers · 1 filter
Ubiquity in graphs II: Ubiquity of graphs with nowhere-linear end structure
Nathan Bowler, Christian Elbracht, Joshua Erde +4
A graph is said to be -ubiquitous, where is the minor relation between graphs, if whenever is a graph with for all , the…
Partitioning edge-coloured infinite complete bipartite graphs into monochromatic paths
Carl Bürger, Max Pitz
In 1978, Richard Rado showed that every edge-coloured complete graph of countably infinite order can be partitioned into monochromatic paths of different colours. He asked whether…
-arc and -circle connected graph-like spaces
Paul Gartside, Max Pitz
A space is -arc connected (respectively, -circle connected) if for any choice of at most points there is an arc (respectively, a circle) in containing the specifi…
Ubiquity in graphs I: Topological ubiquity of trees
Nathan Bowler, Christian Elbracht, Joshua Erde +4
Let be a relation between graphs. We say a graph is \emph{-ubiquitous} if whenever is a graph with for all $n \in \mathb…
Tangles and the Stone-Cech compactification of infinite graphs
Jan Kurkofka, Max Pitz
We show that the tangle space of a graph, which compactifies it, is a quotient of its Stone-Čech remainder obtained by contracting the connected components.
Partitioning Edge-Coloured Complete Symmetric Digraphs into Monochromatic Complete Subgraphs
Carl Bürger, Louis DeBiasio, Hannah Guggiari +1
Let be the complete symmetric digraph on the positive integers. Answering a question of DeBiasio and McKenney, we construct a -colouring of the edges of $K_{\ma…