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
(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
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
Currier-Moore-Yip. YES (L3,L3;R^2). 2024