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Partitioning a 2-edge-coloured graph of minimum degree 2n=3 + o(n) into three monochromatic cycles

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 (2023) Partitioning a 2-edge-coloured graph of minimum degree 2n=3 + o(n) into three monochromatic cycles. European Journal of Combinatorics. ISSN 0195-6698

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Identification Number: 10.1016/j.ejc.2023.103838

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
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: 23 Feb 2024 19:39
URI: http://eprints.lse.ac.uk/id/eprint/120220

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