Graham's boundedness conjecture for Euclidean Ramsey sets
Graham's boundedness conjecture for Euclidean Ramsey sets
A finite set in a Euclidean space is Ramsey if, for every , some dimension contains a monochromatic congruent copy of under every -colouring. Graham's boundedness conjecture. For every , there exists such that whenever is a Ramsey set of size at most in some Euclidean space, every -colouring of contains a monochromatic congruent copy of . This is presented as an open boundedness problem for Ramsey sets.
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Primary source
Rahil Baber, Natalie Behague, Asier Calbet, David Ellis, Joshua Erde, Ron Gray, Maria-Romina Ivan, Barnabás Janzer, Robert Johnson, Luka Milićević, John Talbot, Ta Sheng Tan and Belinda Wickes, “A collection of open problems in celebration of Imre Leader's 60th birthday”, arXiv:2310.18163 (2023).
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