All regular polytopes are Ramsey

DOI10.1016/j.jcta.2006.08.001zbMath1116.05085OpenAlexW2051617766MaRDI QIDQ878959

Kristal Cantwell

Publication date: 4 May 2007

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2006.08.001

zbMATH Keywords

Ramsey theory\(n\)-dimensional polytopesdivision of spacespolyhedra and polytopesquasi-regular polyhedraregular figures

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Polyhedra and polytopes; regular figures, division of spaces (51M20) Ramsey theory (05D10)

Related Items (12)

Upper bounds for the chromatic numbers of Euclidean spaces with forbidden Ramsey sets ⋮ Improvements of the Frankl-Rödl theorem and geometric consequences ⋮ On a Frankl-Rödl theorem and its geometric corollaries ⋮ Two-Colorings of Normed Spaces without Long Monochromatic Unit Arithmetic Progressions ⋮ Max-norm Ramsey theory ⋮ On the chromatic numbers corresponding to exponentially Ramsey sets ⋮ On the Frankl–Rödl theorem ⋮ Transitive sets in Euclidean Ramsey theory ⋮ Exponentially Ramsey sets ⋮ The Hadwiger–Nelson Problem ⋮ Improved Frankl-Rödl theorem and some of its geometric consequences ⋮ All finite sets are Ramsey in the maximum norm

Cites Work

• Euclidean Ramsey theorems. I
• Edge-Ramsey theory
• Permutation Groups in Euclidean Ramsey Theory
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