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PreprintCC BY 4.0arXiv

Monochromatic cycle partitions in 3-mean edge-colourings

  • Csaba Biró
  • Richard Lang
  • Ryan R. Martin
  • Guilherme Oliveira Mota
  • Alexey Pokrovskiy
  • Miklós Ruszinkó
  • Gábor N. Sárközy
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Abstract

Given r ∈ 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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Cite

BibTeXRIS
BibTeX
@misc{biro2026monochromatic,
  title = {{Monochromatic cycle partitions in 3-mean edge-colourings}},
  author = {Csaba Biró and Richard Lang and Ryan R. Martin and Guilherme Oliveira Mota and Alexey Pokrovskiy and Miklós Ruszinkó and Gábor N. Sárközy},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.29336},
  eprint = {2607.29336},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.29336},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Monochromatic cycle partitions in 3-mean edge-colourings
AU  - Csaba Biró
AU  - Richard Lang
AU  - Ryan R. Martin
AU  - Guilherme Oliveira Mota
AU  - Alexey Pokrovskiy
AU  - Miklós Ruszinkó
AU  - Gábor N. Sárközy
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2607.29336
UR  - https://arxiv.org/abs/2607.29336
AB  - Given r ∈ 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.
ER  -