Euclidean Ramsey Theory
Euclidean Ramsey Thms I by Erdos, Graham, Montgomery, Rothchild, Straus, 1973
Euclidean Ramsey Thms II by Erdos + same 5, 1973
Euclidean Ramsey Thm III by + same 5, 1973
Euclidean Ramsey Theorems on the n-Sphere by Graham, 1983
Topics in Euclidean Ramsey Theory by Graham, 1990
Recent trends in Euclidean Ramsey Theory Graham, 1994
Euclidean Ramsey Theory Graham, 2004
Gen. Ramsey Theory for Graphs. II. Small Diag. Numbers by Chvatal and Harary
All Right Triangles are Ramsey. Shader
Chrom Number using subsets of R
(La,Lb;n) means for all 2-col of R^n exists red unit-a-AP or blue unit-b-AP
(La,Xb;n) means for all 2-col of R^n exists red unit-a-AP or blue X-config, and X size b
Erdos et al. NOT: (L6,L6;2). 1973
Juhasz. Yes (L2,X4;2). 1979
Csizmadia-Togh. exists X NOT (L2,X8;2). 1994
Szlam. Yes (L2,X3;2)s. 1999
Arman-Tsaturian. Yes (L2,L6;3). 2017
Tsaturian. Yes (L2,L5;2). 2017
Arman-Tsaturian. Yes (L2,L(n+3);n). 2017
Conlon-Fox. Yes (L2,L(2^{cn};R^n). No on something. 2018
Currie-Mody-Xie-Zhang. No (L2,L6330};R^2). No on something. 2026
slides on Currie-Mody-Xie-Zhang paper
Conlon-Wu. No (L3,L10^50;R^n). 2022
Fuhrer-Toth. No (L3,L1177;R^n). 2024
Currier-Moore-Yip. No (L3,L20;R^n), (L4,L18;R^n)), (L5,L10;R^n). 2024
slides on Currie-Mooore-Yip paper
Currier-Moore-Yip. YES (L3,L3;R^2). 2024
Conlon et al. L colinear or n convex. 2025
Chrom Number of n-dim Euclidean space
Upper Bds on chi(En) in low dim by Arman-Bondarenko-Prymak-Radchenko
The Realization of distances with sets in Euclidean space by Larman-Rogers
A new proof of the L-R up bd for chi(En) by Prosanov
Note on the chi(En) by Radocic-Toth
On the chromatic number of s space by Raigorodskii