Pokrovskiy, Alexey (2019) An approximate version of a conjecture of Aharoni and Berger. Technical Report. Birkbeck College, University of London, London, UK. (Unpublished)
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Abstract
Aharoni and Berger conjectured that in every proper edge-colouring of a bipartite multigraph by n colours with at least n + 1 edges of each colour there is a rainbow matching using every colour. This conjecture generalizes a longstanding problem of Brualdi and Stein about transversals in Latin squares. Here an approximate version of the Aharoni-Berger Conjecture is proved—it is shown that if there are at least n+o(n) edges of each colour in a proper n-edge-colouring of a bipartite multigraph then there is a rainbow matching using every colour.
Metadata
| Item Type: | Monograph (Technical Report) |
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| Additional Information: | Birkbeck Pure Mathematics Preprint Series #52 |
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Depositing User: | Maura Paterson |
| Date Deposited: | 15 Jun 2020 11:03 |
| Last Modified: | 02 Aug 2023 18:00 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/32253 |
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