Induced Ramsey-Type Results and Binary Predicates for Point Sets

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Induced Ramsey-Type Results and Binary Predicates for Point Sets

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Induced Ramsey-Type Results and Binary Predicates for Point Sets

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

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Svazek periodika

2017

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

1-22

Kód UT WoS článku

000414866500003

EID výsledku v databázi Scopus

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