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 (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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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:	24 Oct 2025 18:00
URI:	http://eprints.lse.ac.uk/id/eprint/120220

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