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A proof of Ringel’s conjecture
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Montgomery, R., Pokrovskiy, A. and Sudakov, B. (2021) A proof of Ringel’s conjecture. Geometric and Functional Analysis, 31 (3). pp. 663-720. doi:10.1007/s00039-021-00576-2 ISSN 1016-443X.
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Official URL: http://dx.doi.org/10.1007/s00039-021-00576-2
Abstract
A typical decomposition question asks whether the edges of some graph G can be partitioned into disjoint copies of another graph H. One of the oldest and best known conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with n edges packs 2n+1 times into the complete graph K2n+1. In this paper, we prove this conjecture for large n.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Decomposition (Mathematics), Graph theory, Hypergraphs | ||||||||||||
| Journal or Publication Title: | Geometric and Functional Analysis | ||||||||||||
| Publisher: | Birkhaeuser Verlag AG | ||||||||||||
| ISSN: | 1016-443X | ||||||||||||
| Official Date: | 2 September 2021 | ||||||||||||
| Dates: |
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| Volume: | 31 | ||||||||||||
| Number: | 3 | ||||||||||||
| Page Range: | pp. 663-720 | ||||||||||||
| DOI: | 10.1007/s00039-021-00576-2 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Date of first compliant deposit: | 21 June 2022 | ||||||||||||
| Date of first compliant Open Access: | 22 June 2022 | ||||||||||||
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