10 citations · 14 across the 9 of their papers we have counts for
9 papers
The Lovász-Cherkassky theorem for locally finite graphs with ends
Raphael W. Jacobs, Attila Joó, Paul Knappe +2
Lovász and Cherkassky discovered independently that, if is a finite graph and such that the degree is even for every vertex , t…
A strengthening of Halin's grid theorem
Jan Kurkofka, Ruben Melcher, Max Pitz
We show that for every infinite collection of disjoint equivalent rays in a graph there is a subdivision of the hexagonal half-grid in such that all its verti…
Countably determined ends and graphs
Jan Kurkofka, Ruben Melcher
The directions of an infinite graph are a tangle-like description of its ends: they are choice functions that choose compatibly for all finite vertex sets a c…
Hamiltonicity in infinite tournaments
Ruben Melcher
We prove that for all countable tournaments the recently discovered compactification by their ends and limit edges contains a topological Hamilton path: a topological arc…
Halin's end degree conjecture
Stefan Geschke, Jan Kurkofka, Ruben Melcher +1
An end of a graph is an equivalence class of rays, where two rays are equivalent if there are infinitely many vertex-disjoint paths between them in . The degree of an end is…
Ends of digraphs I: basic theory
Carl Bürger, Ruben Melcher
In a series of three papers we develop an end space theory for directed graphs. As for undirected graphs, the ends of a digraph are points at infinity to which its rays converge. U…
Ends of digraphs II: the topological point of view
Carl Bürger, Ruben Melcher
In a series of three papers we develop an end space theory for digraphs. Here in the second paper we introduce the topological space formed by a digraph together with its…
Ends of digraphs III: normal arborescences
Carl Bürger, Ruben Melcher
In a series of three papers we develop an end space theory for digraphs. Here in the third paper we introduce a concept of depth-first search trees in infinite digraphs, which we c…
Approximating infinite graphs by normal trees
Jan Kurkofka, Ruben Melcher, Max Pitz
We show that every connected graph can be approximated by a normal tree, up to some arbitrarily small error phrased in terms of neighbourhoods around its ends. The existence of suc…