What question did this study set out to answer?

The aim is to investigate Ramsey-type functions related to graphs in Euclidean spaces.

December 22, 2025Open Access

Ramsey problems for graphs in Euclidean spaces and Cartesian powers

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The findings reveal monochromatic properties in graphs, implying novel Ramsey-type characteristics in Euclidean spaces.

The aim is to investigate Ramsey-type functions related to graphs in Euclidean spaces.
Analyzed r-colorings of Euclidean spaces to avoid monochromatic unit-copies of graphs.
Examined chromatic properties of even cycles and forests.
Established connections with Cartesian powers and Turán-type characteristics.
Demonstrated that χ_H(ℝ^n)=χ(ℝ^n) for even cycles of length 8 or 12 and forests.
Showed that χ_H(ℝ^n)=⌊χ(ℝ^n)/2⌋ for sufficiently long odd cycles.
Identified open problems regarding the chromatic number of graph C_4.

Axenovich et al. (2025) studied this question.

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