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