Comptes Rendus
Articles du volume
Combinatoire
More on lines in Euclidean Ramsey theory
David Conlon1  ; Yu-Han Wu2
1 Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
2 École Normale Supérieure - PSL, Paris, France
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 897-901.

Let ℓ m be a sequence of m points on a line with consecutive points at distance one. Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number m and a red/blue-colouring of 𝔼 n for every n that contains no red copy of ℓ 3 and no blue copy of ℓ m .

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.452

David Conlon 1 ; Yu-Han Wu 2

1 Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
2 École Normale Supérieure - PSL, Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2023__361_G5_897_0,
     author = {David Conlon and Yu-Han Wu},
     title = {More on lines in {Euclidean} {Ramsey} theory},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {897--901},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.452},
     language = {en},
}
TY  - JOUR
AU  - David Conlon
AU  - Yu-Han Wu
TI  - More on lines in Euclidean Ramsey theory
JO  - Comptes Rendus. Mathématique
PY  - 2023
SP  - 897
EP  - 901
VL  - 361
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.452
LA  - en
ID  - CRMATH_2023__361_G5_897_0
ER  - 
%0 Journal Article
%A David Conlon
%A Yu-Han Wu
%T More on lines in Euclidean Ramsey theory
%J Comptes Rendus. Mathématique
%D 2023
%P 897-901
%V 361
%I Académie des sciences, Paris
%R 10.5802/crmath.452
%G en
%F CRMATH_2023__361_G5_897_0
David Conlon; Yu-Han Wu. More on lines in Euclidean Ramsey theory. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 897-901. doi : 10.5802/crmath.452. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.452/

[1] Andrii Arman; Sergei Tsaturian Equally spaced collinear points in Euclidean Ramsey theory (2017) (https://arxiv.org/abs/1705.04640)

[2] Andrii Arman; Sergei Tsaturian A result in asymmetric Euclidean Ramsey theory, Discrete Math., Volume 341 (2018) no. 5, pp. 1502-1508 | DOI | Zbl

[3] Saugata Basu; Richard Pollack; Marie-Françoise Roy Algorithms in Real Algebraic Geometry, Algorithms and Computation in Mathematics, 10, Springer, 2006

[4] David Conlon; Jacob Fox Lines in Euclidean Ramsey theory, Discrete Comput. Geom., Volume 61 (2019) no. 1, pp. 218-225 | DOI | Zbl

[5] György Csizmadia; Géza Tóth Note on a Ramsey-type problem in geometry, J. Comb. Theory, Ser. A, Volume 65 (1994) no. 2, pp. 302-306 | DOI | Zbl

[6] Paul Erdős; Ronald L. Graham; Peter Montgomery; Bruce L. Rothschild; Joel Spencer; Ernst G. Straus Euclidean Ramsey theorems I, J. Comb. Theory, Ser. A, Volume 14 (1973), pp. 341-363 | DOI | Zbl

[7] Paul Erdős; Ronald L. Graham; Peter Montgomery; Bruce L. Rothschild; Joel Spencer; Ernst G. Straus Euclidean Ramsey theorems II, Infinite and finite sets (Colloq., Keszthely, 1973), Vol. I (Colloquia Mathematica Societatis János Bolyai), Volume 529, North-Holland, 1973, pp. 529-557

[8] Paul Erdős; Ronald L. Graham; Peter Montgomery; Bruce L. Rothschild; Joel Spencer; Ernst G. Straus Euclidean Ramsey theorems III, Infinite and finite sets (Colloq., Keszthely, 1973), Vol. I (Colloquia Mathematica Societatis János Bolyai), Volume 529, North-Holland, 1973, pp. 559-583

[9] Péter Frankl; Vojtěch Rödl A partition property of simplices in Euclidean space, J. Am. Math. Soc., Volume 3 (1990) no. 1, pp. 1-7 | DOI | Zbl

[10] Péter Frankl; Richard M. Wilson Intersection theorems with geometric consequences, Combinatorica, Volume 1 (1981), pp. 357-368 | DOI | Zbl

[11] Rozalia Juhasz Ramsey type theorems in the plane, J. Comb. Theory, Ser. A, Volume 27 (1979), pp. 152-160 | DOI | Zbl

[12] Igor Kříž Permutation groups in Euclidean Ramsey Theory, Proc. Am. Math. Soc., Volume 112 (1991) no. 3, pp. 899-907 | DOI | Zbl

[13] Arthur D. Szlam Monochromatic translates of configurations in the plane, J. Comb. Theory, Ser. A, Volume 93 (2001) no. 1, pp. 173-176 | DOI | Zbl

[14] Sergei Tsaturian A Euclidean Ramsey result in the plane, Electron. J. Comb., Volume 24 (2017) no. 4, P4.35, 9 pages | Zbl

Cité par Sources :

Commentaires - Politique