Pokrovskiy, Alexey (2014) Partitioning edge-coloured complete graphs into monochromatic cycles and paths. Journal of Combinatorial Theory, Series B 106 , pp. 70-97. ISSN 0095-8956.
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Abstract
A conjecture of Erdős, Gyárfás, and Pyber says that in any edge-colouring of a complete graph with r colours, it is possible to cover all the vertices with r vertex-disjoint monochromatic cycles. So far, this conjecture has been proven only for r = 2. In this paper we show that in fact this conjecture is false for all r > 2. In contrast to this, we show that in any edge-colouring of a complete graph with three colours, it is possible to cover all the vertices with three vertex-disjoint monochromatic paths, proving a particular case of a conjecture due to Gyárfás. As an intermediate result we show that in any edge-colouring of the complete graph with the colours red and blue, it is possible to cover all the vertices with a red path, and a disjoint blue balanced complete bipartite graph.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Research Centres and Institutes: | Applied Macroeconomics, Birkbeck Centre for |
| Depositing User: | Alexey Pokrovskiy |
| Date Deposited: | 12 Dec 2018 16:46 |
| Last Modified: | 06 Aug 2024 20:22 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/24978 |
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