Unavoidable butterfly minors in digraphs of large cycle rank
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916845305462784 |
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| author | Hatzel, Meike Kwon, O-joung Lee, Myounghwan Wiederrecht, Sebastian |
| author_facet | Hatzel, Meike Kwon, O-joung Lee, Myounghwan Wiederrecht, Sebastian |
| contents | Cycle rank is one of the depth parameters for digraphs introduced by Eggan in 1963. We show that there exists a function $f:\mathbb{N}\to \mathbb{N}$ such that every digraph of cycle rank at least $f(k)$ contains a directed cycle chain, a directed ladder, or a directed tree chain of order $k$ as a butterfly minor. We also investigate a new connection between cycle rank and a directed analogue of the weak coloring number of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unavoidable butterfly minors in digraphs of large cycle rank Hatzel, Meike Kwon, O-joung Lee, Myounghwan Wiederrecht, Sebastian Combinatorics Discrete Mathematics Cycle rank is one of the depth parameters for digraphs introduced by Eggan in 1963. We show that there exists a function $f:\mathbb{N}\to \mathbb{N}$ such that every digraph of cycle rank at least $f(k)$ contains a directed cycle chain, a directed ladder, or a directed tree chain of order $k$ as a butterfly minor. We also investigate a new connection between cycle rank and a directed analogue of the weak coloring number of graphs. |
| title | Unavoidable butterfly minors in digraphs of large cycle rank |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2507.11814 |