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

Papers on chi(En): Asymptotic

FW paper, exp lower bound on chi(En)

Raigorodskii paper- slight improvement on FW

LR Paper on exp upper bound on chi(Rn)

Prosanov. A new proof of the LR up bd for chi(En) by Prosanov

Prosanov. chromatic number of spheres

Papers on chi(En): Concrete

Upper Bds on chi(En) in low dim by Arman-Bondarenko-Prymak-Radchenko

RT. chi(E3) LE 15

Chrekaskhin. On the Chrom numb of small-dim E. Spaces

Coulson. 15-coloring of of E3

Coulson. 18-coloring of of E3

Exoo. chi(En) for small n

Exoo. chi(E4)

Kahle. chi(Ed) for d=8,9,10,11,12

Oren. chi(E3) GE 6