An end degree for digraphs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910806662184960 |
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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 |