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arXiv · 2607.29336

Monochromatic cycle partitions in 3-mean edge-colourings

Richard Lang·Guilherme Oliveira Mota
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Abstract

Given $r \in \mathbb{N}$ and an edge-coloured complete graph such that the average number of colours incident with a vertex is at most $r$, Conlon and Stein asked whether there is a vertex partition into a bounded number of monochromatic cycles, and proved this for $r=2$. We settle the first open case by proving the corresponding statement for $r=3$.

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Richard Lang, Guilherme Oliveira Mota. 2026-07-31. Monochromatic cycle partitions in 3-mean edge-colourings. https://arxiv.org/abs/2607.29336

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