An end degree for digraphs

Fuente: arXiv
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Hauptverfasser: Hamann, Matthias, Heuer, Karl
Format: Preprint
Veröffentlicht: 2024
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author Hamann, Matthias
Heuer, Karl
author_facet Hamann, Matthias
Heuer, Karl
contents In this paper we define a degree for ends of infinite digraphs. The well-definedness of our definition in particular resolves a problem by Zuther. Furthermore, we extend our notion of end degree to also respect, among others, the vertices dominating the end, which we denote as combined end degree. Our main result is a characterisation of the combined end degree in terms of certain sequences of vertices, which we call end-exhausting sequences. This establishes a similar, although more complex relationship as known for the combined end degree and end-defining sequences in undirected graphs.
format Preprint
id arxiv_https___arxiv_org_abs_2412_01514
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An end degree for digraphs
Hamann, Matthias
Heuer, Karl
Combinatorics
05C63, 05C20
In this paper we define a degree for ends of infinite digraphs. The well-definedness of our definition in particular resolves a problem by Zuther. Furthermore, we extend our notion of end degree to also respect, among others, the vertices dominating the end, which we denote as combined end degree. Our main result is a characterisation of the combined end degree in terms of certain sequences of vertices, which we call end-exhausting sequences. This establishes a similar, although more complex relationship as known for the combined end degree and end-defining sequences in undirected graphs.
title An end degree for digraphs
topic Combinatorics
05C63, 05C20
url https://arxiv.org/abs/2412.01514