Ramsey upper density of infinite graph factors

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F23%3A00133945" target="_blank" >RIV/00216224:14330/23:00133945 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1215/00192082-10450499" target="_blank" >http://dx.doi.org/10.1215/00192082-10450499</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1215/00192082-10450499" target="_blank" >10.1215/00192082-10450499</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Ramsey upper density of infinite graph factors

Popis výsledku v původním jazyce

The study of upper density problems on Ramsey theory was initiated by Erdos and Galvin in 1993 in the particular case of the infinite path, and by DeBiasio and McKenney in general. In this paper, we are concerned with the following problem: given a fixed finite graph F, what is the largest value of n, such that every 2-edge-coloring of the complete graph on N contains a monochromatic infinite F-factor whose vertex set has upper density at least A? Here we prove a new lower bound for this problem. For some choices of F, including cliques and odd cycles, this new bound is sharp because it matches an older upper bound. For the particular case where F is a triangle, we also give an explicit lower bound of 1- p 1 7 = 0.62203 ... , improving the previous best bound of 3/5.

Název v anglickém jazyce

Ramsey upper density of infinite graph factors

Popis výsledku anglicky

The study of upper density problems on Ramsey theory was initiated by Erdos and Galvin in 1993 in the particular case of the infinite path, and by DeBiasio and McKenney in general. In this paper, we are concerned with the following problem: given a fixed finite graph F, what is the largest value of n, such that every 2-edge-coloring of the complete graph on N contains a monochromatic infinite F-factor whose vertex set has upper density at least A? Here we prove a new lower bound for this problem. For some choices of F, including cliques and odd cycles, this new bound is sharp because it matches an older upper bound. For the particular case where F is a triangle, we also give an explicit lower bound of 1- p 1 7 = 0.62203 ... , improving the previous best bound of 3/5.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Illinois Journal of Mathematics

ISSN

0019-2082

e-ISSN

—

Svazek periodika

67

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

171-184

Kód UT WoS článku

000975697100008

EID výsledku v databázi Scopus

2-s2.0-85159664123