Coloring triangles and rectangles

Jindřich Zapletal

Type: Article

Publication Date: 2023-11-13

Citations: 0

DOI: https://doi.org/10.14712/1213-7243.2023.020

Abstract

It is consistent that ZF+DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles in two-dimensional Euclidean space does not.

Locations

Commentationes Mathematicae Universitatis Carolinae - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Coloring triangles and rectangles	2021	Jindřich Zapletal
+	Coloring the distance graph in three dimensions	2021	Jindřich Zapletal
+	Three-colorings of the Euclidean plane and associated triangles of a prescribed type	2024	Alexander Kharazishvili
+ PDF Chat	Coloring the distance graphs	2023	Jindřich Zapletal
+	Triangles and Vitali sets	2023	Jindřich Zapletal
+	Chromatic numbers of spaces with forbidden monochromatic triangles	2013	А. М. Райгородский D. V. Samirov
+	Polychromatic colorings of rectangular partitions	2008	Darko Dimitrov Elad Aigner‐Horev Roi Krakovski
+	Coloring redundant algebraic hypergraphs	2021	Jindřich Zapletal
+	Coloring redundant algebraic hypergraphs	2021	Jindřich Zapletal
+	On the chromatic number of a space with forbidden equilateral triangle	2014	A. E. Zvonarev А. М. Райгородский D. V. Samirov Александра Андреевна Харламова
+	Refinement of Lower Bounds of the Chromatic Number of a Space with Forbidden One-Color Triangles	2019	A. V. Bobu A. É. Kupriyanov
+	Balanced two-colorings of finite sets in the cube	1988	József Beck
+	Triangles in a complete chromatic graph with three colors	1985	A. W. Goodman
+	Coloring the distance graphs	2022	Jindřich Zapletal
+	COLORING ISOSCELES TRIANGLES IN CHOICELESS SET THEORY	2023	Yuxin Zhou
+	Distance Coloring	2007	Alexa Sharp
+	Computational geometry column 46	2004	Joseph OʼRourke
+	Improvements of the Frankl-Rödl theorem on the number of edges of a hypergraph with forbidden intersections, and their consequences in the problem of finding the chromatic number of a space with forbidden equilateral triangle	2015	A. E. Zvonarev А. М. Райгородский
+	A note on the oriented chromatic number of grids	2004	Andrzej Szepietowski Monika Targan
+	A two-coloring of Cartesian products	1990	E. G. Zelenyuk V. I. Malykhin

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (3)

Action	Title	Year	Authors
+ PDF Chat	Avoidable algebraic subsets of Euclidean space	1999	James H. Schmerl
+ PDF Chat	Countable decompositions ofR 2 andR 3	1990	Paul Erdős Péter Komjáth
+ PDF Chat	Krull dimension in set theory	2023	Jindřich Zapletal