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January 22, 2026MathematicsOpen Access

Jordan Curves: Ramsey Approach and Topology

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Authors

EBEdward BormashenkoAriel University

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Overview

This framework reveals monochromatic triangles in finite point sets on Jordan curves, suggesting extensive combinatorial stability.

Key Points

  • The aim is to explore combinatorial properties of arcs on Jordan curves using Ramsey theory.
  • Developed a topological-combinatorial framework applying Ramsey theory.
  • Performed two-coloring of arcs connecting points on Jordan curves.
  • Investigated configurations of points on Jordan curves for monochromatic triangles.
  • Extended the framework to higher dimensions and included arcs on the Jordan curve.
  • Proved that six points on a Jordan curve contain a monochromatic triangle.
  • Demonstrated that monochromatic triangles persist under homeomorphisms.
  • Established a three-coloring scheme yielding a classical Ramsey result.
  • Showed infinite configurations allow for infinite monochromatic cliques, stable under topological deformations.

Cite This Study

Edward Bormashenko (2026) studied this question.

synapsesocial.com/papers/6971bdcf642b1836717e26dahttps://doi.org/10.3390/math14020351
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