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%3A10363798" target="_blank" >RIV/00216208:11320/17:10363798 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.endm.2017.06.023" target="_blank" >http://dx.doi.org/10.1016/j.endm.2017.06.023</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.endm.2017.06.023" target="_blank" >10.1016/j.endm.2017.06.023</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Induced Ramsey-type results and binary predicates for point sets

Popis výsledku v původním jazyce

Let A and B be two finite sets of points in the plane in general position (neither of these sets contains three collinear points). We say that A lies deep below B if every point from A lies below every line determined by two points from B and every point from B lies above every line determined by two points from A. A point set P is decomposable if either |P|=1 or there is a partition P1 UNION P2 of P into nonempty and decomposable sets such that P1 is to the left of P2 and P1 is deep below P2. Extending a result of Nešetřil and Valtr, we show that for every decomposable point set Q and a positive integer k there is a finite set P of points in the plane in general position that satisfies the following Ramsey-type statement. For any partition C1 UNIONMIDLINE HORIZONTAL ELLIPSISUNION Ck of the pairs of points from P (that is, of the edges of the complete graph on P), there is a subset Q&apos; of P with the same triple-orientations as Q such that all pairs of points from Q&apos; are in the same part Ci. We then use this 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 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 A and B be two finite sets of points in the plane in general position (neither of these sets contains three collinear points). We say that A lies deep below B if every point from A lies below every line determined by two points from B and every point from B lies above every line determined by two points from A. A point set P is decomposable if either |P|=1 or there is a partition P1 UNION P2 of P into nonempty and decomposable sets such that P1 is to the left of P2 and P1 is deep below P2. Extending a result of Nešetřil and Valtr, we show that for every decomposable point set Q and a positive integer k there is a finite set P of points in the plane in general position that satisfies the following Ramsey-type statement. For any partition C1 UNIONMIDLINE HORIZONTAL ELLIPSISUNION Ck of the pairs of points from P (that is, of the edges of the complete graph on P), there is a subset Q&apos; of P with the same triple-orientations as Q such that all pairs of points from Q&apos; are in the same part Ci. We then use this 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 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_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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 Notes in Discrete Mathematics

ISSN

1571-0653

e-ISSN

—

Svazek periodika

2017

Číslo periodika v rámci svazku

61

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

7

Strana od-do

77-83

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85026765695