Trees and treelike structures in dense digraphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2020
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| _version_ | 1866917510293487616 |
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| author | Mycroft, Richard Naia, Tássio |
| author_facet | Mycroft, Richard Naia, Tássio |
| contents | We prove that every oriented tree on $n$ vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on $n$ vertices with minimum semidegree at least $n/2+o(n)$. This can be seen as a directed graph analogue of a well-known theorem of Komlós, Sárközy and Szemerédi. Our result for trees follows from a more general result, allowing the embedding of arbitrary orientations of a much wider class of spanning ``tree-like'' structures, such as collections of at most $O(n^{0.99})$ pairwise vertex-disjoint cycles and subdivisions of graphs $H$ with $|H| < \exp (\sqrt{O(\log n)})$ in which each edge is subdivided at least once. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_09201 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Trees and treelike structures in dense digraphs Mycroft, Richard Naia, Tássio Combinatorics 05C20 We prove that every oriented tree on $n$ vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on $n$ vertices with minimum semidegree at least $n/2+o(n)$. This can be seen as a directed graph analogue of a well-known theorem of Komlós, Sárközy and Szemerédi. Our result for trees follows from a more general result, allowing the embedding of arbitrary orientations of a much wider class of spanning ``tree-like'' structures, such as collections of at most $O(n^{0.99})$ pairwise vertex-disjoint cycles and subdivisions of graphs $H$ with $|H| < \exp (\sqrt{O(\log n)})$ in which each edge is subdivided at least once. |
| title | Trees and treelike structures in dense digraphs |
| topic | Combinatorics 05C20 |
| url | https://arxiv.org/abs/2012.09201 |