Induced Ramsey-Type Results and Binary Predicates for Point Sets

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10363797" target="_blank" >RIV/00216208:11320/17:10363797 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Induced Ramsey-Type Results and Binary Predicates for Point Sets

Original language description

Let k and p be positive integers and let Q be a finite point set in general position in the plane. We say that Q is (k,p)-Ramsey if there is a finite point set P such that for every k-coloring c of (P choose p) there is a subset Q&apos; of P such that Q&apos; and Q have the same order type and (Q&apos; choose p) is monochromatic in c. Nešetřil and Valtr proved that for every k ELEMENT OF N, all point sets are (k,1)-Ramsey. They also proved that for every k GREATER-THAN OR EQUAL TO 2 and p GREATER-THAN OR EQUAL TO 2, there are point sets that are not (k,p)-Ramsey. As our main result, we introduce a new family of (k,2)-Ramsey point sets, extending a result of Nešetřil and Valtr. We then use this new result to show that for every k there is a point set P such that no function Γ that maps ordered pairs of distinct points from P to a set of size k can satisfy the following &quot;local consistency&quot; property: if Γ attains the same values on two ordered triples of points from P, then these triples have the same orientation. Intuitively, this implies that there cannot be such a function that is defined locally and determines the orientation of point triples.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

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

Name of the periodical

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

—

Volume of the periodical

2017

Issue of the periodical within the volume

24

Country of publishing house

US - UNITED STATES

Number of pages

22

Pages from-to

1-22

UT code for WoS article

000414866500003

EID of the result in the Scopus database

—