Ramsey upper density of infinite graph factors
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Ramsey upper density of infinite graph factors
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Illinois Journal of Mathematics
ISSN
0019-2082
e-ISSN
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Volume of the periodical
67
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
171-184
UT code for WoS article
000975697100008
EID of the result in the Scopus database
2-s2.0-85159664123