Monochromatic triangles in two-colored plane

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A10050551" target="_blank" >RIV/00216208:11320/09:10050551 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Monochromatic triangles in two-colored plane

Original language description

We prove that for any partition of the plane into a closed set C and an open set O and for any configuration T of three points, there is a translated and rotated copy of T contained in C or in O. We also show that for any polygonal partition and any configuration T which is a vertex set of a non-equilateral triangle there is a copy of T contained in the interior of one of the two partition classes. Furthermore, we characterize the polygonal partitions that avoid copies of a given equilateral triple.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Combinatorica

ISSN

0209-9683

e-ISSN

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Volume of the periodical

29

Issue of the periodical within the volume

6

Country of publishing house

DE - GERMANY

Number of pages

20

Pages from-to

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UT code for WoS article

000274206100005

EID of the result in the Scopus database

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