An approximate version of a conjecture of Aharoni and Berger
Pokrovskiy, Alexey (2018) An approximate version of a conjecture of Aharoni and Berger. Advances in Mathematics 333 , pp. 1197-1241. ISSN 0001-8708.
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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 AharoniBerger 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: | Article |
|---|---|
| Keyword(s) / Subject(s): | Latin squares, Rainbow matchings, Connectedness |
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Depositing User: | Alexey Pokrovskiy |
| Date Deposited: | 12 Dec 2018 16:51 |
| Last Modified: | 02 Aug 2023 17:47 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/25436 |
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