The Rainbow Arborescence Problem on Cycles
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915661661339648 |
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| author | Bérczi, Kristóf Király, Tamás Yamaguchi, Yutaro Yokoi, Yu |
| author_facet | Bérczi, Kristóf Király, Tamás Yamaguchi, Yutaro Yokoi, Yu |
| contents | The rainbow arborescence conjecture posits that if the arcs of a directed graph with $n$ vertices are colored by $n-1$ colors such that each color class forms a spanning arborescence, then there is a spanning arborescence that contains exactly one arc of every color. We prove that the conjecture is true if the underlying undirected graph is a cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Rainbow Arborescence Problem on Cycles Bérczi, Kristóf Király, Tamás Yamaguchi, Yutaro Yokoi, Yu Combinatorics Discrete Mathematics The rainbow arborescence conjecture posits that if the arcs of a directed graph with $n$ vertices are colored by $n-1$ colors such that each color class forms a spanning arborescence, then there is a spanning arborescence that contains exactly one arc of every color. We prove that the conjecture is true if the underlying undirected graph is a cycle. |
| title | The Rainbow Arborescence Problem on Cycles |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2511.04953 |