2020/09/07 by Carl Bürger, Bürger, Carl, Ruben Melcher +1
Computer Science · Mathematics · #05C20 #05C38 #05C63 #05C75 #05C78 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2009.03295
openalex publication_date 2020/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. Unlike for undirected graphs, some ends are joined by limit edges; these are crucial for obtaining the end space of a digraph as a natural (inverse) limit of its finite contraction minors. As our main result in this first paper of our series we show that the notion of directions of an undirected graph, a tangle-like description of its ends, extends to digraphs: there is a one-to-one correspondence between the `directions' of a digraph and its ends and limit edges. In the course of this we extend to digraphs a number of fundamental tools and techniques for the study of ends of graphs, such as the star-comb lemma and Schmidt's ranking of rayless graphs.