Minimum sets forcing monochromatic triangles

被引:0
|
作者
Bialostocki, Arie [1 ]
Nielsen, Mark J. [1 ]
机构
[1] Univ Idaho, Moscow, ID 83843 USA
关键词
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The fundamental problem in Euclidean Ramsey theory is the following: Given a configuration C of points in R-n and an arbitrary k-coloring of R-n, does there exist a monochromatic set of points in R-n congruent to C? In this paper we focus on the case where k = n = 2 and C is the vertex set of a triangle. We will say that a triangle T is 2-Ramsey if every 2-coloring of R-2 gives a monochromatic set congruent to the vertex set of T. The foundations of Euclidean Ramsey theory were laid in a sequence of three seminal papers [2], [3], and [4]. Among the many results of these papers, the authors make the following conjecture:
引用
收藏
页码:297 / 303
页数:7
相关论文
共 50 条
  • [1] Almost empty monochromatic triangles in planar point sets
    Basu, Deepan
    Basu, Kinjal
    Bhattacharya, Bhaswar B.
    Das, Sandip
    DISCRETE APPLIED MATHEMATICS, 2016, 210 : 207 - 213
  • [2] Monochromatic empty triangles in two-colored point sets
    Pach, Janos
    Toth, Geza
    DISCRETE APPLIED MATHEMATICS, 2013, 161 (09) : 1259 - 1261
  • [3] ON MONOCHROMATIC TRIANGLES
    BORWEIN, PB
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 1984, 37 (02) : 200 - 204
  • [4] On Almost Empty Monochromatic Triangles and Convex Quadrilaterals in Colored Point Sets
    Jorge Cravioto-Lagos
    Alejandro Corinto González-Martínez
    Toshinori Sakai
    Jorge Urrutia
    Graphs and Combinatorics, 2019, 35 : 1475 - 1493
  • [5] On Almost Empty Monochromatic Triangles and Convex Quadrilaterals in Colored Point Sets
    Cravioto-Lagos, Jorge
    Corinto Gonzalez-Martinez, Alejandro
    Sakai, Toshinori
    Urrutia, Jorge
    GRAPHS AND COMBINATORICS, 2019, 35 (06) : 1475 - 1493
  • [6] Zero forcing sets and the minimum rank of graphs
    Barioli, Francesco
    Barrett, Wayne
    Butler, Steve
    Cioaba, Sebastian M.
    Cvetkovic, Dragos
    Fallat, Shaun M.
    Godsil, Chris
    Haemers, Willem
    Hogben, Leslie
    Mikkelson, Rana
    Narayan, Sivaram
    Pryporova, Olga
    Sciriha, Irene
    So, Wasin
    Stevanovic, Dragan
    van der Holst, Hein
    Vander Meulen, Kevin N.
    Wehe, Amy Wangsness
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (07) : 1628 - 1648
  • [7] On minimum rank and zero forcing sets of a graph
    Huang, Liang-Hao
    Chang, Gerard J.
    Yeh, Hong-Gwa
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (11) : 2961 - 2973
  • [8] Empty monochromatic triangles
    Aichholzer, Oswin
    Fabila-Monroy, Ruy
    Flores-Penaloza, David
    Hackl, Thomas
    Huemer, Clemens
    Urrutia, Jorge
    COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2009, 42 (09): : 934 - 938
  • [9] MONOCHROMATIC TRIANGLES IN 3 COLORS
    SANE, SS
    WALLIS, WD
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1988, 37 (02) : 197 - 212
  • [10] FORCING QUASIRANDOMNESS WITH TRIANGLES
    Reiher, Christian
    Schacht, Mathias
    FORUM OF MATHEMATICS SIGMA, 2019, 7