Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia
ORCID: 0000-0002-4104-3635, Lang, Richard, Skokan, Jozef
ORCID: 0000-0003-3996-7676 and Stein, Maya
(2024)
Partitioning a 2-edge-coloured graph of minimum degree 2n/3 + o(n) into three monochromatic cycles.
European Journal of Combinatorics, 121.
ISSN 0195-6698
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Text (0195-6698)
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Abstract
Lehel conjectured in the 1970s that the vertices of every red and blue edge-coloured complete graph can be partitioned into two monochromatic cycles. This was confirmed in 2010 by Bessy and Thomassé. However, the host graph G does not have to be complete. It suffices to require that G has minimum degree at least 3n/4, where n is the order of G, as was shown recently by Letzter, confirming a conjecture of Balogh, Barát, Gerbner, Gyárfás and Sárközy. This degree condition is tight. Here we continue this line of research, by proving that for every red and blue edge-colouring of an n-vertex graph of minimum degree at least 2n/3+o(n), there is a partition of the vertex set into three monochromatic cycles. This approximately verifies a conjecture of Pokrovskiy and is essentially tight.
Item Type: | Article |
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Official URL: | https://www.sciencedirect.com/journal/european-jou... |
Additional Information: | © 2023 Elsevier |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 18 Sep 2023 09:24 |
Last Modified: | 16 Aug 2024 10:51 |
URI: | http://eprints.lse.ac.uk/id/eprint/120220 |
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