Monochromatic triangles in the max-norm plane

被引:0
作者
Natalchenko, Alexander [1 ]
Sagdeev, Arsenii [2 ]
机构
[1] MIPT, Moscow, Russia
[2] Alfred Reny Inst Math, Budapest, Hungary
关键词
DISTANCE GRAPHS; CHROMATIC NUMBER; RAMSEY; SETS;
D O I
10.1016/j.ejc.2024.103977
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For all non -degenerate triangles T , we determine the minimum number of colors needed to color the plane such that no max -norm isometric copy of T is monochromatic. (c) 2024 Elsevier Ltd. All rights reserved.
引用
收藏
页数:11
相关论文
共 32 条
[1]  
Aichholzer O., 2019, 35 EUR WORKSH COMP G
[2]   Distance graphs and T-coloring [J].
Chang, GJ ;
Liu, DDF ;
Zhu, XD .
JOURNAL OF COMBINATORIAL THEORY SERIES B, 1999, 75 (02) :259-269
[3]  
Cheng XB, 2023, Arxiv, DOI [arXiv:2305.18218, 10.1007/s00454-024-00693-3, DOI 10.1007/S00454-024-00693-3]
[4]   On the chromatic numbers of small-dimensional Euclidean spaces [J].
Cherkashin, Danila ;
Kulikov, Anatoly ;
Raigorodskii, Andrei .
DISCRETE APPLIED MATHEMATICS, 2018, 243 :125-131
[5]  
CHILAKAMARRI KB, 1991, GEOMETRIAE DEDICATA, V37, P345
[6]  
Currier G, 2024, Arxiv, DOI [arXiv:2402.14197, 10.48550/arXiv.2402.14197,arXiv, DOI 10.48550/ARXIV.2402.14197,ARXIV]
[7]  
de Grey A., 2018, Geombinatorics, V28, P559
[8]  
DEBRUIJN NG, 1951, NEDERL AKAD WETENS A, V54, P371, DOI DOI 10.1016/S1385-7258(51)50053-7
[9]  
Erdos P., 1975, C MATH SOC J BOLYAI, V10, P559
[10]  
Erdos P., 1973, J COMBIN THEORY A, V14, P341