Year: 2020
Type: preprint
Abstract: 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 call normal spanning arborescences. We show that normal spanning arborescences are end-faithful: every end of the digraph is represented by exactly one ray in the normal spanning arborescence that starts from the root. We further show that this bijection extends to a homeomorphism between the end space of a digraph $D$, which may include limit edges between ends, and the end space of any normal arborescence with limit edges induced from $D$. Finally we prove a Jung-type criterion for the existence of normal spanning arborescences.
Source: arXiv (Cornell University)
Authors: Bürger, Carl, Melcher, Ruben
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3083764684