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Monochromatic triangles in the max-norm plane

Combinatorics 2024-07-04 v2 Metric Geometry
Authors: Alexander Natalchenko , Arsenii Sagdeev
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Abstract

For all non-degenerate triangles T, we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of T is monochromatic.

Keywords

ramsey theory and colorings

Cite

@article{arxiv.2302.09972,
  title  = {Monochromatic triangles in the max-norm plane},
  author = {Alexander Natalchenko and Arsenii Sagdeev},
  journal= {arXiv preprint arXiv:2302.09972},
  year   = {2024}
}

Comments

10 pages, 4 figures; v2 includes a few modifications based on the reviews

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R2 v1 2026-06-28T08:44:31.725Z